@Chris Dee
So presuming your state works the way mine does, and I expect it would. I understand this element of agency law is pretty typical.
You can't force him to write an offer for you. He's not obligated. In fact, he *can't* submit an offer for you because you won't sign his agreement.
He showed you the house already. Agents *can* show houses without a signed agreement. But the reason they might not is that it gives them less protection in terms of being able to guarantee themselves any compensation for the work they're doing showing homes. But this agent did show you the home without a written agreement.
Unfortunately for you, an agreement beforehand would have done more to protect *you*. Because now the agent is your procuring cause in the purchase, should you go on to buy that particular house. They'd have a strong claim for compensation.
Something else you should consider here is that it's possible you read the contract incorrectly. Most contracts state something to the effe t of "compensation due to agent shall be_____________" and then they have filled in "3% of final sales price" or whatever their number is. And you read that part of the contract and think that it means you owe that money. If you read through the remainder of the compensation section, however,it says that the agent will first seek that amount from the listing agent or seller. In this case, a number like 3% is what the contract states, you *are* ultimately responsible for it, but won't have to worry about paying it so long as the listing offers a sufficient commission to cover it.