Aris, the reason you're having a problem with my answers is because I don't think you are considering how frickin complicated language is, and why certain things may or may not be called certain things. Language is a reflection of thoughts...kind of. And kind of not. Part of its content exists outside our thoughts, maybe in the noosphere or whatever. This is not a trivial topic. If someone approaches you, says the child is his son, and asks me "so am I his parent", the only thing I could answer is "what kind of information are you looking for in my answer?" If they wanted me to acknowledge that they love their son, I'd say sure (if that's true). If they want me to understand that there's a blood relationship, I'd say ok, I guess if you're the father then that's what you are. If they want me to understand that they brought up the child, I'd say ok, that's the term we'll use to mean that. But in all these cases something different is meant by me agreeing. You want me to just agree as if the content of my agreement is immaterial. What you want is a blanket statement saying "ok, whatever you want me to mean, you can pretend I meant, so long as I agree to your term usage." Well if I care about whether actual true information is being passed, then I'd want to know what the meaning is of what I'm agreeing to. Just agreeing to use a term without regard to its meaning sounds dangerous to me.
Now this may or may not be parallel to the gender pronoun issue. In the case of parent/child terms, there is a definite meaning baked in to the use of the term that is mutually understandable; whether it's "this is my legal heir", or "we love him as if he's our own". Whatever the meaning is, it should be fairly clear in that sense what is meant by using the same word (parent) in a way that can potentially mean various things. With gender pronouns I don't think that's the case the trans community is making. I think the case being made is that it's a subjective evaluation that in fact does not require me to understand the why of it, or for there to be a common meaning to the term. It's not supposed to be communicative, just a matter of respect. There is no social or structural interrelationship in play defining the context of the term use; it's a purely personal matter, divorced from its relationship to others. So in that respect alone I don't think these two uses of terms map onto each other.
I hope what wasn't too much "babble" for you. Did you know that it takes exponentially more space to unpack a claim than it takes to make one? But please go ahead and call an attempt to make sense of the situation "babble." Sounds to me like trying to shame someone into backing off.