First of why doesn’t he offer the house wrap? If you are the one paying the bill any good contractor should give you what you want, not what they want. I would recommend you tell him you want the house wrap (and any other features you want incorporated into YOUR house) or you will use another contractor. I believe he may reconsider offering the house wrap.

The use of house wrap under siding is a very useful thing provided it is installed correctly. All joints and openings around doors, windows, etc., should be taped to provide a good tight seal. It will keep the wind from blowing through the walls. Siding is not a perfect seal from air infiltration. The house wrap takes care of any air leaking in around the siding to keep it from entering the house.

I run into this type of thing all the time and it really ticks me off. I am willing to listen to any advice someone may have to offer, but in the end, as long as I am paying the bill, I will decide how to spend the money and there is no room for discussion. Give me what I want for my money or I will find someone who will.

I may have come off a little strong here, but I have strong feelings about this type of thing. Especially when it comes to something that is as large an investment as a house.

Is the biggest concern about not using Tyvek more of an air infiltration issue or should I be more concerned about water getting in and damaging the OSB board under the siding?

The main purpose of a building wrap is air infiltration. It will help some to protect the OSB board but that is a secondary benefit.