I think there is more to this than buying a bike.
First off he took bikes lessons but wasn't going to buy a bike? Pull the other one it has bells on it. Naive as that makes you that you believed him.
He lied to you.
He went out bike searching. He lied by omission.
He was talking about bikes on the pc. He lied to you.
He arranged insurance and actually bought a bike. He lied to you.
He decided that you not wanting him to have a bike due to what you have seen was unimportant. Your opinion was unimportant. The fact that you would consider this a valid reason to leave him was unimportant. Does that mean he considers your relationship unimportant?
Do you have joint finances that he has decided he is entitled to a chunk from to buy a bike, tax and insure it, plus all the safety wear he will need.
He is also looking at mortgages without your knowledge. Does he want out of your relationship and this is his way of starting to tell you? Was he planning on getting a house and moving out or telling you that you and DD were moving with him done deal?
I would pack your bags and go to your parents for the weekend and have a long think calmly without an argument. Is the getting the bike a deal breaker or all the lying and devious behaviour and lack of caring about your opinions?
I am a biker BTW.