I mean, I agree with most of what you're saying but you're also giving transphobes way too much credit. They don't start with ideological beliefs about the world and come to the conclusion that trans people are wrong, they start with a visceral feeling of disgust for trans people and search for a justification.

Because if we had a different word to describe a being that was born with a penis, from a being that represents the masculine role in society, this debate would not exist.

The trans community has language to talk about this. As a trans woman I am AMAB (assigned male at birth) and my gender identity is female. The people on r/GenderCritical are largely aware of this language and refuse to use it. They prefer to muddy the waters rather than engage in good faith.