Besides, Cloud feels responsible for getting Aerith into trouble in the first place -- because she went with him, she got caught.
Cloud didn't care about saving the world when Barret explained the situation to him during the bombing mission. He cared about getting paid.
Cloud didn't care about the heat brought on the inhabitants of the sector when he bombed the reactor. All he cared about was getting the job done.
Aeris get's captured... Cloud develops a guilt complex? Nah that just doesn't wash with me. Don't get me wrong I'm not denying CxT, but Aeris is getting some special treatment there. Why?
Also, they did it to hinder Shinra's plans for her. They're mission statement is to screw Shinra over whenever possible. Besides, Barret is the leader of the group still, and he says he owes it to rescue her because she saved Marlene. It's all there in the game.
So if Barret's ordering Cloud why doesn't Cloud charge him like the first mission?