Wesley, aka Giotto, did insult Kirk by calling him Dunsel. Maybe he thought Kirk was too pissed and wanted revenge: a dish best servedcooold.

Though not a favorite episode, I'm never disliked "The Ultimate Computer". But you've made me realize just how
contrived
it is.
Basically, writers decide how they want their story to end, arranging things so that it does. This is not in and of itself wrong. A famous book on the psychology of drama emphasizes that the characters' motives, personalities, conflicts,
etc
, must be consistent with the story's progression and ending you can't superimpose any ending on any story.
In short, all stories are contrived, in some way or another. The problem is hiding the seams. "The Ultimate Computer" fails to do this, and we're left with significant unanswered questions.
In the novelization of
2001
, Clarke directly addresses the question of why HAL goes bonkers. On a less-profound level, Isaac Asimov, in his robot stories, explains that each command given a robot sets up an electrical potential in its "brain", and the levels of such potentials strongly affect its behavior when confronted with conflicting situations.

most realistic episode. no aliens who like exactly like humans and speak English

But Wesley and Kirk supposedly knew each other well. Right away he assumes Kirk is Crazy? Some friend. Kirk on the other hand knows that if the ship looked vulnerable that Wesley wouldn't fire. Kirk had a lot more faith in Wesley than Wesley had in him.
He's taking the knife out of the Cheese!
Do you think he wants some cheese?

Because he can't assume the computer's gone bad. It's aggressive action that needs to be dealt with. He did try to communicate with the Enterprise and Kirk.

Yes, there did seem to be quite a few stories where some agency took complete control of the ship from one small section.

Oh, and why not turn off - or otherwise disable - the weapons systems? Even if M5 had some kind of protective shield around itself, I don't recall any evidence that they would have been unable to turn off power to or otherwise the main phasers themselves, or the photon torpedo launchers. They seemed to have ample time, considering everything else they were doing.

there is that odd scene where Daystrom and the M-5 are talking to each other how great they both are that at a certain moment I was expecting them to exchange Hi-5 's with each other.

"No, no, no, no! Let me have it have it for awhile Let me work with it for awhile! Please! Please!"
Send her to the snakes!

Actually, I don't see it so much as weak writing, but as something that probably wasn't totally explained well enough. Remember it's television. We can assume that Commodore Wesley got a rather pat briefing on the M-5, a general summary of what it could do, in that it was meant to be able to control most of the functions of a starship without a larger crew, but still in general control by command staff on the ship. After all, he didn't see the M-5 in action. This was a first trial run of the M-5 under both standard and combat conditions of a starship.
Certainly he could not have known that Dr. Daystrom created the M-5 to make human-like decisions, and thus used his own engrams as a pattern for how the M-5 thinks. I mean, that's not something that would be in the brochure. Maybe it wouldn't have affected his decision on this matter, but it would've given me a bit of pause, at least to run some simulations first, which was probably done.
So if I expected to be shot at with weak phasers and I got full phasers instead, I'd probably initially wonder what's going on with Kirk. It would be natural to make such an assumption if he was wasn't totally privy to the details.

Actually I use mostly "retired" high-end business systems, HP/Dell rackmount "Servers," etc. Plus a few that I built myself.
My current "desktop" system that I use for online chatting, email, etc - including these boards - is a Dell R710, dual quad-core 2.93ghz, with 7 drives installed out of a possible 8. About 2.5tb total space. It initially cost me $175 without the drives. Some business probably paid close to $8,000 for it new. And it's not THAT old. Plus those systems are commonly "retired" from situations like server farms where they had full air conditioning/cleaning, stable power In many ways they're still practically new condition.

You have an Apple ?
(I have a HAL wallpaper on my laptop )

My computers never have "ERRORS." They are always "fully operational."

Cool. A guy I went to college with had Nomad going "ERRORS, ERRORS" on his computer. I never knew what it was from until I saw that ep on BBCA.
Always remember to keep Ridin The Storm Out, people!

For many years, my computer's start-up sound was HAL 9000 saying "I am completely operational, and all of my circuits are functioning perfectly."

I sorta wondered about that, too. That commodore guy had known Kirk for a long time, right? He should have figured it out. They could have done it like "I don't want to kill Enterprise's crew, but that computer has got to be stopped!".
Since I saw that ep I call my laptop "M-5" whenever it acts up.
Always remember to keep Ridin The Storm Out, people!

They might assume that the "off" switch ALWAYS works.
Although as McCoy pointed out:
McCOY: Fantastic machine, the M-5.
No "off" switch.

That has bothered me too over the years, but they might have easily assumed, without the direct experience that the Enterprise has had by then, that M-5 couldn't possibly just take over completely. They might assume that the "off" switch ALWAYS works.
But even with that said, it's hard to figure why they'd think Kirk was somehow responsible.