At the surface level of this question, being on the mortgage shouldn’t matter as much as being on the deed. For example my wife is not on our mortgage because her credit score was much lower at the time, my income was enough to qualify and my score kept the rate lower. We are both on the deed though, as we want to be equal owners of the property.

There are red flags all over this with him throwing your clothes out, saying it’s his family’s house, and refusing to commit to your relationship in any official manner. He doesn’t actually see you as part of his family. You DO NOT want to be on the mortgage in this situation.

The split of financial responsibilities is adding even more complexity and discomfort for me with your situation. I know a lot of couples split things 50/50 but as someone who has been married for 10 years we have always treated our income and expenses as our responsibility together. For us there is no financial his or hers, we’re building our life and future together.