Nope, abort mission, abort mission. A disbelief in something that basic implies some worrisome things about her or her family. End the date, the relationship, and run the other way.

Don't move past it. If she doesn't accept reality, that's on her. If you choose to join her, that and the consequences are on you.

If she's really a lesbian, then why did she agree to go out on a date with you in the first place? Did she misunderstand and think that you were just hanging out as friends? Did you say something offensive so that she said that she's lesbian in order to ensure that you will not pursue her romantically any further? It sounds like there's more to this story than you know (or more than you're telling us).

Did she know it was a date?

I feel like we need a little more info but based on what you wrote. 1. She just thought you were hanging out and she didn’t think it was a date. And then realized that you thought it was a date so she told you she was gay. 2. The date was so bad that she told you she was gay so you wouldn’t ask her out again. Hopefully it was the first one. But if it was the second one she could have been honest just said this isn’t working out, let’s just be friends.

Why would she even go on a date with you if she was a lesbian?

Did she know you were a man?

guessing she's trying to find a way to say "this isn't working for me" and/or she's just a straight-up b!tch