The most important thing to know about Juror #7 is that he doesn't really care about justice and wants to reach a verdict ASAP so he can get to a baseball game. This is pretty much the first thing we learn about him when he says, "OK, men. Let's take our seats, huh? We can all get out of here pretty quick. I have tickets to that ball game tonight. Yanks and Cleveland. We've got this kid Modjelewski in there."
Juror #7 knows full well that he doesn't care about the verdict, but at least in the beginning, he pretends to be offended when someone questions his motives. He shows this offense when he says, "What, just because I voted fast? I think the guy's guilty. You couldn't change my mind if you talked for a hundred years." The ironic thing here is that #7 will change his mind more easily than anyone else in the room. He's just saying whatever he thinks will get the verdict over with as soon as possible.
By the midway point of the movie, #7 has started saying stuff like, "Do me a favor. Wake me up when this is over." He even gets to a breaking point when he says, "Listen. I'll tell you something. I'm a little sick of this whole thing already. We're getting nowhere fast. Let's break it up and go home. I'm changing my vote to not guilty." So in other words, he's totally willing to admit to the whole room that he doesn't care if the defendant is guilty or innocent. He just wants to go home. And we should remind you here that the defendant will get the DEATH PENALTY if he's convicted, so it's fair to say that Juror #7 is about as selfish as a human being can be.