I've been reading about this and thinking about how I found my closest friends. They kinda just 'happened'. You can't really force a friendship, it's something that happens, or doesn't, when you talk to people. I wonder if you're having trouble because you're trying a little too hard.
Let's see....one friend and I started talking because we were the two oldest people in a college class. That just started the conversation, gave us something to talk about that day. We kept talking, and are still talking 30 years later.
Another friend I met because she was hanging out with someone I knew from college orientation. I went up to say hi to the girl I knew, and ended up talking to the people who were with her, and found that this other girl liked the same kind of movies I do. We still go see movies together 35 years later.
I wasn't looking to make friends in either case. Just livin' my life. And that's how you'll find friends, too. You can't make it happen, you'll just run into people that you'll hit it off with. Don't press. When you meet new people, just strike up a conversation. Ask them a question about themselves. Everybody likes to talk about themselves.

Just something to get the conversation started. Like "what school do you go to?" If it's someone in one of your classes, you have plenty of conversation material. "What did you think of the homework yesterday?"
And since you mentioned being sarcastic, competitive, and insulting, I'll just say that those things are kinda tricky, and can kill a friendship before it starts. I can be sarcastic with my friends and pick on them but that's because I've known them forever and I know their sense of humor, and I know where the line is between something they'll laugh at and something that'll hurt their feelings. I'd never, never be insulting with someone I'd just met and didn't know well.
Competitive...does that mean that you like to play games and compete, or that you get really mad and throw things and yell when you lose? Again, it can go both ways. Competing can be lots of fun between friends. Being a poor loser...well, nobody likes being around someone like that.