Why does my friend like being single so much?

Probably past relationships. If that's not the case, she might want to keep her virginity until marriage. I'm a single 19 year old guy, I don't have a girlfriend because I know I need to mature before jumping into a relationship.

The more someone tries to push me to do something, the more I don't want to do it.
This applies here, even though your her friend you should understand that maybe she doesn't want a relationship of that kind at this age.

Really I would question why she should be in a hurry to chase down a boyfriend. If the right guy comes along, she will probably naturally jump but if she is everything that you described she should not have to go after a guy and she can be very choosy if she wishes (which I imagine she is.) I would not rush into a relationship for the sake of getting into a relationship. You can have a great deal of fun in life without being tied down to one person (especially when you are young.) If she realizes this, perhaps this is why she "doesn't care."

Maybe, just maybe, she wants to develop herself instead of trying to spend all her time chasing after some guy she won't even know a year from now. Look at how you described her - wow, looks like she's making something of herself. She'll find a guy when her time comes.

Besides, lots of people feel miserable when they are in relationships because the relationship is founded on the concept of having to be in one as opposed to finding the right person. I think she is commendable for making herself into a complete person rather than trying to find someone to validate her.

So many relationships are riddled with problems and stress and you're friend might just like her freedom of being able to do whatever she wants whenver she wants.