Because he was offended by his infidelity. It fits perfectly with the morals at the time. Simple as that.

I watched again and I saw no indication of homosexuality. If he knew Alec was married and also slept with men, why would he seem disappointed that he had hidden depths after finding the scarf?
Then Alec says he's 'sorry because the situation must seem vulgar to him, actually it isn't in the least'.

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Maybe Americans aren't understanding British sarcasm, where he's angry but he's being sarcastic by pretending he isn't when picking up the scarf and realising his friend had lied to him.

I believe that Noel Coward's original story, on which the film was based, involved two men - one married, one not, but at that time, homosexuality was illegal in Britain, and it could never have been portrayed that way on film.
The scene with Stephen makes a bit more sense if viewed with that in mind, but with the translation to a heterosexual love affair, it could have been worded in a way more in tune with the rewrite.
As Producer, perhaps it was Coward's way of sending a signal to the gay world

I think Stephen was obviously a homosexual and that this was intended to be obvious without being express.
As for the affair between them, I think Lean intended the audience to draw its own conclusions. You can't really be sure, but I tend to think that there is no way Stephen would be so "disappointed" by this silly fling, even if it was in his bachelor pad.
People back in the 40s, on both sides of the pond, may have acted very prim and proper, but they were only keeping up appearances. Infidelity was as rampant then as it is now. Stephen, being a presumably non-monogamous homosexual in a time where this was still extremely taboo, could not possibly have been outraged by the idea that his friend was being promiscuous behind his wife's back. He even said he was a man of the world and that no explanations were necessary.
So then, what disappointed Stephen so? Why that look on Alec's face and that tone in his voice when he says "You're really angry, aren't you?"
In my estimation, there is, at the very least, a crush which both men are aware of and, perhaps, a sexual history.
In any case, I think it's quite naive to suggest that this is all merely some trite expression of moral indignation on the part of Stephen. He's no angel himself, by the standards of the era, so he has no lesson to give Alec on sexual morality.

1. As mentioned elsewhere, Stephen would have had a right to be perfectly outraged that Alec had failed in his role of filling in for him at the hospital. Not just once, but 6 or 7 times I think. But we don't know for sure if he ever found out about that. My guess is that someone at the hospital would be sure to tell him sooner or later.
2. Stephen presumably still needs a person to fill in for him if he intends to take Thursdays off in future, so we are left wondering what will happen to that little arrangement. Except that Alec is leaving England anyway.
3. I think that Stephen
   is
   probably meant to be gay. Alec probably
   isn't
   overtly, but there may be some "frisson" between them, which has probably never come to anything.
4. Stephen is not Noel Coward. Noel Coward was the station announcer! (Yes, listen carefully next time you see it. I discovered this on a visit to Carnforth Station. They have a museum and heritage centre, and a refreshment room done out like the one in the film, although those scenes were not actually filmed on the station, but in studio mock-ups at Denham Studios.
   (OK, I know the comment about Stephen being NC was not meant literally).
5. Being British myself, I wish to counter those comments which emphasise the supposed respectability of the British upper-middle classes of that era.
   First, this film may have been set in the late 1930s (I have seen 1939 suggested), but it was actually made in 1945. If nothing else, the war had probably begun to alter radically the supposed moral standards of pre-war years. People didn't know how long they were going to be alive, and were probably more likely to take a risk and enjoy their pleasures today and not worry about tomorrow.
   But even back in the 1930s, I don't think the British Upper-Middle-Classes were so very "moral". They may have had a veneer of respectability, but that's another thing. You only have to read the novels of Evelyn Waugh to see how much marital infidelity there was. In fact, these people could probably get away with it far more easily than lower class people, since they had the resources. For example they could afford to take hotel rooms, or carry on affairs under the covers of large weekend house parties, etc.
   One would have to be discreet, of course, but that was something they were very good at.

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Both of those pieces of information are very interesting. I know I'm years late, but do you think Trevor Howard would have identified that as a flaw because he missed the homosexual subtext, or for another reason? On first viewing I was simply surprised by Stephen's overtly prudish behaviour, but a second and third viewing, and this thread, has me convinced of the homosexual angle - which adds so much to the film really.

I think it was because we didn't see Alec's wife even though we saw Laura's husband, so his friend was the one who we saw the reaction from on his side.

I just watched BRIEF ENCOUNTER again for the first time (not including the Hallmark remake) in forty years. Maybe I'm delusional, but I recall a scene at the hospital not from Ms. Jesson's POV but from Dr. Harvey's when Dr. Lynn offers Alec the key and explains why. I believe Stephen even went as so far as to suggest Alec entertain a lady friend if he wished, but it seemed a code for encouraging homosexual behavior and perhaps Stephen's opportunity to meet new men as well through Alec. Later I read a film critique which substantiated this interpretation.
I also vividly remember Trevor Howard being on a talk show in the '70s reacting to the usual flattery about this film in regard to its scripting. He himself pointed out how he felt Dr. Lynn's change in behavior completely belied the original offer to use the flat; Howard said he saw that as the film's sole flaw.
I sincerely doubt I hallucinated both the film sequence and the interview.

As someone who is old fashioned and who understands the morality and way of life of the 1940s rather well, I simply see the friends 'anger' as common sense.
It is how I would react, it is disappointment in a friend, disgust, etc.
I would react like that if I simply heard one of my friends was having an affair, let alone if he wanted to use my apartment for it.
Civilised decent people do not have affairs, so if your friend does, you are disappointed and upset.
I don't see any kind of gay subtext, even if there was, it has little to do with why he was angry.
How much motivation does one need to be mad with a friend behaving in such a manner?

A further thought on this scene, which struck me, when I first saw the movie: Is the purpose of the scene, and the haughty distaste, shown by the other doctor (I've always referred to him as "the other doctor") to remind us that this is two stories in one; a love affair, that ends in frustration, and a betrayal of a decent husband by his errant wife (a sordid escapade, as the other doctor might have it)? We aren't forced to chose, but we will likely do so in the course of the movie.

He's an old fashioned prig. Times have changed, divorce wasn't sanctioned by the church back then and adultry was really frowned upon that class (the middle class). The fact that it was clandestine and involved his friend, in as much as he would have to look the other way, was tantamount to making him an accessory to something sordid. The homosexual angle is barking up the wrong tree, but very modern or current. The idea that there might be repressed homosexuality is open to speculation (Coward was homosexual. I don't know much about Lean.), but speculation here misses the point. I may be the only one, but I at least find the friends adhearance to principle, however sanctimonious, admirable.

I didn't see any gay subtext, and even though part of the resentment might be a crush on Alec, I think it's a matter of Stephen being annoyed that Alec was going to use his place for an affair that could possibly result in a public scandal.
Revenge is a dish that best goes stale.

I also thought that the friend was homosexual and feeling slightly jilted. I don't think there was ever any relationship between them however. I agree with other posters that we shouldn't read too much 2010 culture and preconceptions into the story, but even allowing for the English culture of 1945, I think the hint of homosexuality was clear.

• henry

I think people see what they want to see, depending upon their own leanings. For me, I would agree that I would find it distasteful, the idea of a friend bringing a lover and possibly "using" my bed, especially without asking me first (which I would reject.)

Well, I read Stephen as gay for sure. I don't know why he couldn't have been, having been created by Noel Coward and all. If Lean/Coward were anything like Hitchcock then I feel sure there may have purposely been something coded to escape censorship.
OTOH, I had no reason to think the two men were having an affair or that Stephen was jealous. Interesting and arguable take though, IMO.

When watching the scene the thought of Steve being gay struck my mind as well. With his mannerism and talking about being a man of the world. Still I didn't see them having an affair or anything. Also I believed him when he said he didn't mind what was going on precisely because he understands love need to hide sometimes.
I think he was sore, because his friend wouldn't trust him and be honest with him. That's how I, being gay, having straight friends, would feel.

But Stephen could have just shrugged it off in a more good-natured way, realizing that affairs happen. His stuffy reaction sucked, to coin a phrase.

My guess is that Stephen IS Noel Coward. And dirtying someone's sheets without their permission is bad form, at the very least.

I agree with SusanHampson. We must interpret the scene having in account that was England in the 40s, so that would be a normal reaction.
Maybe in today standards seems weird, but things were really different back there.

"I didn't think he was gay, just a Brit from the 30s/40s. Almost all of them seemed gay, didn't they?"
No, only to USians, especially ones who go on about Brits rather than Englishmen, Scotsmen et al, many such USians still think "Brits" seem "gay", as well as thinking there is something wrong with being homosexual.
"Nothings gonna change my world!"

Whew! When that poster said it was obvious Stephen was gay and he and Alec were having an affair, and then several people concurred that feeling, I thought I was going crazy!!
I didn't think he was gay, just a Brit from the 30s/40s. Almost all of them seemed gay, didn't they?
I thought he was just disapproving of Alec's infidelity, and resented that he was using his apartment for the tryst.
It's possible Stephen was gay, but even so, they weren't having an affair. As the other poster said, he just had a crush on his friend.
I agree with the English poster earlier. I think it's just hard for us Americans, especially in 2009, to picture things being so strict and proper once upon a time.
"I'm not trying to get in the middle of 'crazy'."