Why does this older man keep calling me a girl?

It's hard to know what term(s) of address are appropriate since it varies so much from person to person. I doubt very much that he means any offense, and he might well cringe himself if he knew it made you cringe. I have inadvertently offended people too and have always been grateful for finding out.

You are entitled to be addresed in a manner that makes you comfortable, but he is entitled to know that you are not comfortable with things as they are as well.

Just tell him, in a non-judgemental way, ideally in person, what your preference is, and I would expect that problem will soon be over. I don't see any reason to stop working with him, if he is responsive to your request.

If not, there's a bigger issue. Which, come to think of it, there might be since you did mention that you don't like him that much and it's not clear whether that's because of the way he addresses you or because of something else..