Sounds about right to me.
So many stories, so little time.

I always thought it was a commentary on the politics of the time. During the Cold War, the big fear was man destroying humanity with nuclear weapons.

Then he probably went back to his misanthropic ways at the end.

That in itself is rather ironic considering how he started the film hating Humanity and trying to find something better.

He spent the second half of the movie defending the human race, be it on Earth or on a distant planet.

He already knew he was alive thousands years from anything he knew. He also knew he couldn't get back. That his own generation destroyed itself shouldn't have mattered so much.

You're right, Taylor jumps to the conclusion that man has destroyed himself with nuclear weapons without any implicit evidence that that is actually what happened. But Zaius does imply quite exactly that his breed made a desert of the Forbidden Zone ages ago, so it's a reasonable conclusion on Taylor's part, and it's certainly what the filmmakers wanted the audience conclusion to be.

Taylor didn't know about the cave's destruction. Zaius didn't even tell Cornelius and Zira about his plans until Taylor was on his way to the statue.

HE WAS talking about man destroying himself.
If those pen pushers up at city hall don't like it,well, they swivel on this middle digit!

If you're thinking of Taylor's line "You blew it up!" he wasn't referring to man destroying himself with atomic bombs, but of Dr Zaius blowing up the cave that contained the evidence that modern ape sprang from man and not vice versa.

And the correct one.

I agree they are all good points. However there is no proof that man in Taylor's time blew himself up instead of some natural calamity knocking man back to the Stone Age. I think it's just Taylor's natural dour attitude that makes him jump to this conclusion.

Zaius told Taylor "The Forbidden Zone was once a paradise. Your breed made a desert of it, ages ago". And the Statue of Liberty looked pretty singed.

Taylor instantly jumps to the conclusion that his Humanity destroyed itself with atomic weapons when their was plenty of evidence that some natural calamity had wiped out modern civilisation
Actually, there wasn't "plenty of evidence" of either. All that is seen is the result, not the cause. Taylor comes to the conclusion that he does because he knows about the planet from his time.
much like the giant asteroid wiped out the dinosaurs
Any asteroid that big would wipe out all humans and all apes.

Yes I understand that. However Taylor instantly jumps to the conclusion that his Humanity destroyed itself with atomic weapons when their was plenty of evidence that some natural calamity had wiped out modern civilisation allowing for the apes to rise, much like the giant asteroid wiped out the dinosaurs allowing mammals to take a foothold. Why the instant conclusion from Taylor, or was it just his cynical nature perhaps?

Exactly right!

Up until he discovered the statue, he'd believed he was on another planet formerly inhabited by a different race of intelligent humans. Zaius insisted that those humans had been evil and Taylor was defending them, as there was no direct evidence that they were belligerent.
But after reaching Lady Liberty, not only did he realize he was home all the time, but that Zaius was right.