What made Apollo change his mind about wanting a rematch?

I think it was when people where saying Rocky was robbed and should of won the first fight.

When Apollo said "There can be no rematch." it was immediately after the final bell, and before the results were known. He probably assumed at that point that he would win by unanimous decision, and everyone would agree with that decision. Then when it was announced as a split decision, he realized that not only had one of the professional judges thought he lost the fight, but that a lot of people who watched would also think so. Then as time went on and the hate mail and sportscasters kept questioning who really should have won, his pride finally got the better of him. He knew the only way to put the matter to bed would be to have rematch, and this time actually take Rocky seriously.

I always figured that when they made the original, they didn’t know they would do a sequel involving a rematch. So they had Apollo say, “there won’t be a rematch.” But plans changed. So they had Apollo renege

Are you stupid or something? It's well established in the movie. Unlike Adrian's change of mind.

He probably changed his mind because of more $$$$$, plus, he was intrigued by his opponent

Multiple reasons.....

1. When he says no rematch, he just went 15 rounds. Was exausted and had broken Ribs and swelling on this face....He was not in the right mindset and needed medical attention.

2. He did not win the fight unanimously. One of the judges voted for Rocky winning the fight (This hurt Apollos Ego)

3. He got a ton of hate mail from Fans that say he lost and it pissed him off and hurt his ego more.

4. Rocky was the only person Apollo Did NOT beat. He won, but he did not beat him. Apollo was Angry.

Guessing you dozed off during the scene when Apollo was reading all of his "ROCKY WON, YOU BUM" hate mail to his wife.

Ego.

He (kind of) admitted defeat (or at very least equality) at the end of the first fight with his "Don't want one" response, to commentators immediate question of a rematch?

But then (after hate-mail) and introspection, he realised he'd initially taken Balboa lightly...and needed to prove himself, despite Duke being content with the 'win' (he sort of concedes to such in subsequent movies)

This trait seemed to be his default flaw in the franchise.