You Are Never Obligated To Sell to a Given Offer

Must you sell if you list at a specific price and the broker comes up with a qualified buyer?

in the US in general, no you do not have to sell, but you could still be liable to the broker for their commission. You might also need to justify why your decision was non-discriminatory (assuming that it wasn't), but if (for instance) your broker brings you someone you have had business dealings with in the past, and they have tried every manouever possible to scam you after reaching agreement in those past dealings, you are (usually) quite justified in refusing to do business with them.

Talk to a lawyer, but generally speaking, if you do not have complete and perfect agreement between the parties on the contract, you do not have a valid purchase contract, and if you didn't want to do business with (say) Bill Clinton or George W. Bush, such is your right as long as you refuse to do so on the basis of them being a particular individual, not based upon them being members of a class protected under anti-discrimination law.

In general, nobody can force you to sell. But it can be expensive not to. I am not familiar with any cases where a real estate agent, listing or buyer's, was awarded a commission even though there was no transaction consummated, but that doesn't mean it couldn't happen. Refusing to sell on the basis of race, sex, religion, sexual orientation, or lifestyle is setting yourself up for a lawsuit.

On the other hand, just because someone offers you full list price does not mean you have to accept it. If the other terms are onerous, if it comes attached with conditions you don't care to accept, or if it is merely from an individual who you have done business with in the past and are unwilling to be involved with again, you are usually within your rights to refuse the offer.

Caveat Emptor