Because it makes the EU look evil, and remaining looks like submitting to bullies.

The EU is a protectionist island in a global economy filled with large ambivalent actors. It's less evil, more like self-preservation, or an immune system. There has to be surface tension to retain mass, and there has to be barriers because that's it's raison d'etre.

I understand the game theory, but I think politically, it would be easy to spin this as the EU being a bully who punishes you if you don't play with them, and many voters would prefer to tell such a bully to bugger off than to play along (indeed, a lot of the Leave campaign was already about how Brussels bullies Brits into doing things they don't want).

To echo the other poster - because it looks like the actions of an empire-building bully. It looks like spite.

Because, as it was also seen in the US election, it wasn't possible for them to win.

It will be interesting to watch, nothing has been negotiated, that's the irony, nobody even knows what they voted for. I can't imagine Europe making it easy though.

I don't see how it was impossible for Remain to win. There was <4% margin; different turnout demographics could have swung it. I can imagine holding it a week earlier or later could have led to a different result.