does he not trust me?

the father of my child is now pushing for a DNA test. my family suggests its because he doesnt trust me. I know 100% its his child. im jusst conflicted if im gonna be taking it to far to tell him if we are not in a relationship and he does not trust me then he needs to back off and mind his own business when it comes to me, my finances and moves.

this situation has arisen and im starting to think he really does not trust me now because he is questioning whether i was rude to his mother or not? now i talk openly to him but i would never make the owner of the house feel some type of way esp since she opened her home to me when my options of places to stay are so limited

my question is:

is this because of lack of trust?

am i taking things to far?

and what would you do in my situation? (his mother basically telling me to leave because I "disrespected" her ( called her by her first name for about 4 months and she is juss addressing this and saying shes not my maid because I left dishes in the sink when I went to work that I routinely clean when I get off work but I guess shes thinking I left them there for her. Again none of these issues were addressed until 4 months later)