"I'm sorry but I don't give free cards to 3 other players on the flop with a board like this one. And neither should you."

You're not giving a free card, you're taking one. The continuation bet takes this pot down on the flop just about never. You more than likely do not have the best hand, equity-wise, at the moment. You need to improve to win. It is checked to you. Why on earth would betting be superior to taking the free card here?