Ichigo fights to protect people he cares about, plain and simple.
His mother was killed by a hollow when he was young, so he tries his best to prevent something like that from happening to anyone ever again. He said to Rukia in the first chapter that he wasn't a superhero who could protect everyone, yet he also wasn't an egoistic brat who wouldn't protect people he could save.
When Orihime was attacked by the hollow of his brother, he berated it for not doing what older brothers are supposed to do. He said that 'older brothers are born first to protect the sisters that come after him'.
When Ishida used the hollow bait to attract hollows, he was angry because Ishida dangered all of the inhabitants of Karakura just for a challenge. If he, as Lord Raine says, fights for the sake of fighting he wouldn't give shit about other people and would unnecessarily prolong the fighting.
Ichigo went through one hell of a training, had his soul chain severed, and was hollowified in order to get enough power to save Rukia. He feels indebted to her because she's the one who gave him enough power to protect the people around him.
Ultimately that is what Ichigo gets his power from, he trains and works in order to save the people he loves. He doesn't fight for the sake of fighting. He's not like Kenpachi who only cares about fighting strong opponents (even then that's doubtful, because I'm pretty sure that if he had the choice between saving Yashiru or fighting the zeroth espada he'd choose the former in a heartbeat)