You did not say whether you are sexually attracted to homosexual men or if you simply find that you get a long better with them compared to heterosexual men. Some women find that with regard to compatibility and interests, they believe they have more in common with a homosexual male than a heterosexual. Homosexual males may have many of the same interests that females do. These interests can include liking the same types of movies, going shopping, exercising, and so forth. I have often heard females discussing homosexual men in this way “why do all of the great guys turn out to be gay?” Perhaps you prefer the company of homosexual males over heterosexuals because you share many similar interests.
You said that your mother asked you if you are a lesbian. You did not however state in your letter if this is a possibility. If you’re not sexually attracted to females then it would be difficult to conclude that you’re a lesbian. If you are attracted to males but not the heterosexual males that you have met then perhaps you have not found the right heterosexual male. It may be that of the men you have known thus far, none share your interests nor have you found one you are sexually attracted to.
It is also possible that you like the company of homosexual men because you find them less threatening than heterosexual males. Perhaps some aspect of dating and relationships is frightening for you and spending your time with a gay male allows you to avoid relationships. Have you considered this possibility?
Other women who enjoy the company of homosexual men often say they prefer gay bars over “regular” bars. They say that they can have fun and “relax” in the gay bar knowing they will not have to tolerate guys coming on to them. This is another example of why some women like spending time with gay men.
I have listed a few possible reasons that may explain why you feel attracted to gay males but please know that without more detailed information, it is difficult to answer this question with clarity and accuracy. I would need to gather a great deal of information from you in person to fully understand this situation.
I suggest that this is a question you should explore further with a therapist if you feel comfortable doing so. I am suggesting counseling because you seem to feel that your situation is hopeless (“lose-lose” as you said). I do not think this is at all true. A therapist can help you explore your feelings regarding relationships, sexuality and can offer advice on how to find a life partner. Please consider counseling. A good therapist could be helpful to you.