If (real if) you're hostile to the idea that they could really be trans, it's possible they feel hostile to the idea that you could really be making a good faith best effort to support them, which is what this sounds like to me: defensiveness.
True, you don't know me.
When my child came out as pan, a few days later we had arranged for a trip to an old friend of mine who is a trans-woman, a lesbian, and who had a non-binary friend who was staying with her.
I regret the fact that you had a difficult relationship with your parents. I've seen that story play out. However I'm pretty confident that I'm not actually transphobic. My concern is not that I don't want a child who is trans, my concern is about what is best for my child's long-term well-being.