Here's why:
* Steve is a Soc. He's on the opposing side of the rumble, and there's no indication that he'd be willing to betray his group.
* Steve is a coward. He's shown to be more interested in protecting himself than fighting for his side. In fact, he leaves the rumble altogether before it even starts.
If you are remembering something different, you may be thinking of another character or a different part of the story. Let me know if you'd like more details about the rumble or any other aspect of *The Outsiders*.