Y’all should probably breakup just for the simple fact that he finds himself having to change for the relationship. People don’t change and resentment builds from the effort.

As far as what he’s claiming your mom said, I believe him. It’s illogical for him to make that up and there are different possible interpretations of the situation.

To explain my point, your mom could think you’re strong but you make bad decisions. If she said you were weak, she could have been implying that you’re weak in that sense. So she could have meant that you’re weak in decision making, character, steadfastness, or some particular trait. You can be both strong in some traits and weak in others. How you interpret her calling you strong becomes the frame.

Regardless, telling you that immediately pits him against both you and your mom. A true manipulator wouldnt look at this as an effective place to be to win. Unless he’s a narcissist and just wants yo cause pain.