Extended family

Maybe you just came on too strong? It seems strange to me to suddenly want to be close with a cousin when you never were before - like you don't have a family of your own so you expected to just step into theirs? You can't force a relationship like that, which is what it sounds like you may have been trying to do and that may have made them feel uncomfortable. It's understandable that the rejection hurts but if they are not interested in forming a close relationship, that is their choice. I think they were trying to be polite about it but you couldn't take the hint.

You say you have no siblings or children and you're single - what about friends? It sounds like you're kind of lonely, which is understandable, but they have no obligation to bring you into their family because of it.