Would this be a red flag for you?

Would it be a red flag if a man you are seeing says he is desperate for a relationship because it has basically been 7 years. He also told me that when he was 17/18 he was accused of rape and the woman stopped talking to him, then a few months later a cop showed up to his work which caused him to get fired. He did not get in legal trouble. That concerns me a bit.

He has been very, very sweet to me. Understanding of my boundaries and willing to go slow with me. I don’t want my overanalytical brain to get the best of me. However, him saying he was desperate made me question if he’s only willing to go slow because of that. He is very eager to spend time with me and said he thinks about me a lot. We have been on 2 dates, been talking over a month.