I have no idea, go make a thread for it. I'm sure there will be ample reasons why this could be though.

I didn't have him in my party at that time. But he still comes and everything goes on the same way. It is always like this when you have more characters in total than in party.
I never actually seen a game in which either making choices (aside of Dating Sim games) or having different party affects the main plot

No offense, but I used Cait Sith only a few times for a few minutes because I just didn't like him, so he wasn't in my party when the place went kablooey. Regardless, as others have mentioned, he comes back

He calls, the temple turns into black materia, and then cait sith 2.0 comes while cloud is smacking Aerith. So either way he dies. But what really got me wondering was when he said "Try to remember me, even if another cait sith comes along." What do you think he meant by that?

Either he was joking to make Cloud and the party feel sad and weep over his loss, or he was refering to that version of Cait Sith. Cait Sith 1.0 was no more, and Cait Sith says to miss him.

I don't think its ever made clear the extent of Reeves control over Cait Sith, or the way that Reeve controls Cait Sith. Cait Sith appears to have a personality distinct from Reeve, so either Reeve is choosing to have Cait Sith talk and act how he does because he thinks it is funny and suits him, or the toy somehow has a distinct personality.

Either way I can imagine Reeve grew fond of Cait Sith 1.0 . It's like if you play with toys when you are a child and give them a personality, if they break or are lost it really hurts you, and even a replacement that is exactly the same isn't quite the same toy that you gave that personality to.

It's just like, just before he dies, he says "there's plenty stuffed toys like my body around, but there is only one me". And that is pretty much it right there.

Brilliant scene in my opinion.