He has no idea what this peninsula is but apparently it was enough to give Strange somewhat of a big head. Then again, everything gave Strange a big head.

He's itching to fight now but he's not allowed to and he would never take that first attack anyways. Finding powerful people always made him want to at least have a go or two with them.

"Alas, it's not really up to me whether or not you get to die right now. As for her... " He starts to say something but then he just doesn't. Strange didn't need to know the reason why the Prince invited everyone here. The seed of doubt would work just as well, "It doesn't matter. It'll all come to fruition sooner than later."