AITA for letting her pay?

I recently took a woman on a date. We met on tinder, I asked her out, she bailed on our date 3 times, then finally we met up. I picked her up, took her to Jekyll island and I paid the $10 to get on the island. The date seemed to be going great. We went all around the island, went to the pier, driftwood beach, and then left to go get some dinner. I kissed her while on the beach and she kissed me back. Held her hand in the car. We were in and out of the car all day and I opened and closed her door every time. Tried to be as much of a gentleman as possible because I really liked her. We get to dinner, eat, all is well. The check comes and is given to me, I pull out my wallet to pay, she says “here, I got it”, I say no it’s fine I got it. She replies “you paid for us to get on the island let me get it” so instead of arguing with her on our first date I let her pay. I take her home and on the ride home she’s not nearly as energetic as she had been before dinner. I drop her off, no kiss, whatever no big deal. I text her later that I enjoyed our date and hope to see her again. From the way she texts she’s clearly upset about something. I ask her what’s up and she explains to me how it was ridiculous that she had to pay for dinner. Even though I feel I am not in the wrong here, I apologized to her several times, explained what happened, told my point of view, told her I had every intention of paying but she’s still mad. I went on a weekend trip and she said we’ll figure this out when I get back. 3 days later I text her and she is still mad. I told her that if she reacts to something this minuscule like this, then I can’t imagine how she would react to something more serious. I told her I no longer have any desire to see her again. Am I in the wrong?