What the facts are, in transition, may not be terribly useful to know at times. Labelling yourself bi-gendered, gender-fluid, androgynous, mtf, ftm, or anything else is really a way of expressing to others what you are. You don't need a label for yourself... you just want one because everyone expects one.
If being male makes you happy, then you should pursue that. Hormone treatment tends to be pretty good at diagnosing whether someone is really trans or not, so there's no real far of going too far - go as far as you need to to be happy, regardless of what someone else will say.
I will admit that sometimes I'm unsure of what I am. However, what I'm doing is making me happier, and the road ahead of me is exciting... and I expect it will make me happier still. I've also taken the risk out of it - if I turn out to be male after all, then at least I got my SRS, among other things. I enjoy presenting as female, but if I were a guy, I'd still enjoy presenting femininely - and I definitely don't want my penis, whether I'm male or female.
That might sound confusing, I suppose... Eventually, I'd end up with still wanting boobs, facial surgery, hormones, and body/facial hair gone even if I decide I want to be a guy. I take those steps one at a time - every one of them makes me happy. I don't do things because they're a part of the process, but rather because things become necessary for me.
If you feel you need to make changes, or to go as far as to transition to living as male... then that's what you should do, and to hell with everything else.
... That said, if you can be happy as you are, then by all means, don't change a thing.
My opinion? Your therapist is too old-school.