Guys, is it possible to reject a girl, when she asks you out, even though you like her?

No.

This makes no sense. And sense is the domain of men; it's the world we live in.

If you like a girl, and she likes you, and she makes it perfectly, undeliably, crystal clear, and offers a date or relationship, what would you do?

The conditions are as follows:

If you like a girl and a date is offered, you accept.

Lg & Do --> A

and on that note; the contrapositive:

If you do not accept, then it is not the case that you like the girl and a date was offered.

~A --> ~(Lg & Do) [Hence the confusion when playing hard-to-get]

If you don't like a girl and a date is offered, you reject.

~Lg & Do --> R

and on that note; the contrapositive:

If you do not reject, then it is not the case that you do not like the girl and a date was offered.

~R --> ~(~Lg & Do)

What's important is the direction of the conditionals. For example.

If it rains, then the sidewalk will be wet.

R --> W

The sidewalk is wet! Does that mean it rained? No! Maybe it snowed and the snow melted. Maybe a bum took a leak. But if we know that the sidewalk is NOT wet, then we know for sure, that it did NOT rain. For had it rained, we know for sure that the sidewalk would be wet! But the sidewalk may still be wet for many reasons other than rain. This is why Rain is simply SUFFICIENT for the sidwalk to get wet, not NECESSARY. In other words, "if" it rains then the sidewalk is wet, NOT "only if" it rains will the sidewalk be wet.

The more interesting question then is if the conditions for accepting or rejecting a date are "if", "only if", or "if and only if" statements. I'll save you a lot of time and tell you they're "if" statements. Liking you is only one of many reasons a person would either accept or reject you. Maybe they don't like you, but they want to have sex with you. Maybe they don't like you, but you have a lot of money to offer them. So the conditionals mentioned above are most definitely SUFFICIENT, "if" statements.

Now, the more interesting question we're left with is if he "Rejected you" (R), or if he simply "didn't accept" (~A). If he rejected you, logically, we can't "conclude" anything. If we knew he didn't like you and that you asked him out on a date, we could conclude that he would reject you. But we can't conclude him not liking you from him rejecting you (maybe he did, but he just came out of a difficult relationship, maybe there was s/o else, maybe he was hurt by some cold heartless b*tch and has entered an emotionally unavailable sex-only recovery period and doesn't want to hurt you; because he genuinely likes you and cares about you) The point is, we can't conclude anything if he REJECTED you.

But if he simply "didn't accept" (~A), your offer, we can come to a valid conclusion. We can conclude that:

"It is not the case that he does NOT like you AND that you made a perfectly clear offer to ask him on a date or make a relationship serious or official"

Make what you will of that; but that's all we can conclude

When I was in high school and in my first year of college, I had low self-esteem from telling myself how no girl would want me. So when girls asked me out, I said "no" to avoid the perceived feelings of eventually being hurt.

As to your questions of a different nature, I'm not sure I'd want a girl if I had a girlfriend or she had a boyfriend. Guys won't reject you just because they don't want a relationship; that type of guy will say "yes" and then push for sex.