Good lord- people on here can be really loopy! Reading through this, I am imagining a bunch of women at home, sitting on front of their computers, clutching their pearls at the very THOUGHT that he would even ask to go condom free!
It is not unreasonable at all for him to ASK whether you would consider an alternative method. He is not asking you to go cold turkey, or to take the risk, but just feeling you out to see whether something else may work for you both.
If you say no outright and he continues to press on, THEN AND ONLY THEN is he being unreasonable!
I personally hate condoms and was up to the clinic and tested with my (now husband) as soon as we had that chat. Which was about two weeks into sexual exclusivity.
Naturally, you need to get tested if you are going to pull the condom plug, and so does he. I would recommend getting tested now, anyway, as sti's can be caught through oral sex and mutual masturbation, and some sti's can get passed on even when using condoms (crabs, herpes, genital warts, sometimes but very rarely, syphillis).
Getting tested early and routinely is very important for both of you.
Don't ditch him for asking, unless he is a knob moving forward, which is doesn't sound like he is!