No, he killed Zexion under Saix's orders. Saix believed that Zexion was getting in the way of their own plot to overthrow Xemnas.
What are you talking about?! That's a PERFECTLY legitimate reason!
s1gildragonin30years
Might I point out that this was NOT a decision that Axel made lightly? In fact, extra scenes in Final Mix, further elaboration in the novels, and even the regular scenes from KH2 show just how much he was struggling with those orders. Xemnas and Xaldin flat-out said that Roxas needed to be eliminated; Axel then proceeded to lie to their faces and said that Roxas wasn't a traitor, he simply couldn't come back to them yet. Basically, he was lying to protect his friend, and tried to buy them some more time. When that didn't work, he still changed the wording of Xemnas' orders, and told Roxas that he wouldn't get destroyed if he just agreed to come back. I don't think many other members of the Organization would've continuously provided Roxas with that option.
I also firmly believe (and passages from the novels back me up on this) that Axel wasn't really trying his hardest in that last duel. He was angry and aggressive, yes, but it seemed like misdirected anger to me. He was getting increasingly frustrated with how things were going. He didn't want to kill Roxas, but he didn't want to leave the Organization either. He just wanted to go back to the way things were, and neither Xemnas or Roxas was going to let that happen, so Axel finally snapped. But he never really tried to kill Roxas, because he just couldn't do it in the end.
This is why a lot of people, myself included, like Axel, because there's a lot more to him than meets the eye. He's more complex and human than a large amount of the cast, being forced to make extremely difficult decisions. He's a naturally selfish individual, so once he starts actually caring about someone (namely, Roxas and Xion) it really throws him and he doesn't know the right way to act. He makes a lot of mistakes but he's genuinely sorry when things go wrong and keeps on fighting even when he knows it's futile. That's why I like him.