A free trade agreement does not require being in the EU. So of course they want one. The EU saying no is there way of punishing the UK, and discouraging any other nations from leaving. Hmmm. Freedom of choice indeed.
"there way of punishing the UK" Look, If you are going to have a divorce and tell your wife: "Look, we are going to have a divorce but I don't want to pay alimony and we are going to stay fuck buddies and the cottage in Italy that you inherited from your parents, I am still going to use this."
Then all this sounds like an excellent idea but if your wife says "I pass" this does not mean that your wife is going to "punish you". She is just passing on the deal.