Hi and welcome!
Example: Last night he accused me of being mean to him and asked me why I'm so nice to everyone else but not to him. And I told him that I love him but that I also care for other people. He continually asked why and repeats the question.
Rather than trying to answer his question try using validation techniques. Or, to be more accurate,
Don't Be Invalidating. A lot of us are invalidating when that is the last thing we think we are doing.
In your example, he believes that you are nicer to other people than him. That is his feeling and so that is his reality. For pwBPD, feelings = facts. By saying "I love you" you are invalidating his feelings and his sense of reality. I know you are trying to reassure him, I am just talking about how it is most likely coming across to him. Rather than saying I love you, say "oh wow, I hate it when I feel like that and I would be asking about it too'. (or whatever is true for you). You are not agreeing with him, you are not saying his reality is true... and you are not invalidating him by denying what he thinks is true.
What do you think?