I've had friends behave the same way, and it annoyed me too. The subtle implication seems to be that they experience gender dysphoria too, and that I'm crazy for wanting to transition while they just shrug it off and get on with life.
It trivializes what we go through and is patronizingly self-centred and presumptuous, and I'm reminded of that South Park episode when Stan finally realizes why Token is upset with him, and they make peace when Stan says "I get it... I DON'T get it".
My mother has been doing the same thing with me, and it's driving me nuts. Much like your friend and many other cis people, my mother has a big ego, fragile pride, a persecution complex, and they get defensive when they're told others have bigger problems than they do and that, no, their "help" isn't helpful.