Am I just not cut out for relationships?

I'm the only one of my friends without a boyfriend. If a guy flirts with me in public (rare), I get uncomfortable. I'm a really shy person, but I guess I'm also arrogant. The only kind of guys that approach me seem too formulaic. For example, I was in a store and a guy who worked there started walking up to me, and I knew he was going to ask me if I had a boyfriend, I could feel it. So I started trying to walk away and he asked, and I was stuck in the conversation. I hate those conversations. "Do you have a boyfriend?" "No" "Do you want to go eat sometime?" etc., and I can just imagine what would happen. We'd go to some chain restaurant, and he would make "safe" conversation, and anything I said that he doesn't fit with my gender would clify me as a weirdo, and the conversation would involve lots of lame flirting that I would have a hard time participating in, and maybe he'd talk about his family and it would become immediately obvious that he's too conservative, or whatever else, and I'd feel uncomfortable. Or worse yet, what if he actually did understand me, and I felt boring, like I had nothing to add to the conversation? Some of my friends' boyfriends are overtly ist, and my friends just don't see it. I wouldn't be able to take that. I'm not talking about like seeing a turtle and a guy going "he's so cute" and me flipping out on him with, "he? why does it have to be 'he'?" ... I'm talking about realistic things, based in reality, that are ist and ridiculous. I mean, if any of my friends' boyfriends asked me on a date in some alternate universe, I would run away, because they're all vulgar and subtly (some overtly) ist in countless ways. So how am I ever supposed to get a boyfriend?