Yeeeea. I don't blame her for getting pissed at him. He keeps spouting off about how "It's dangerous!", "You shouldn't go!", "It's a trap!" without ever giving a reason why. No shit it is dangerous and a trap, she isn't stupid and obviously knows this. That said it is a situation that has to be dealt with before it blows up into something bigger. Telling her it is dangerous, but now WHY it is dangerous is useless and makes him a shitty guard IMO. If they were in hostile territory and there wasn't time to explain that is one thing, but he doesn't seem to have any good reason why he can't aside from personal reasons.
Even more so that the Duke has approved/allowed her to take this action. It would be one thing if she was sneaking off behind the duke's back, but this is effectively an official Castiello family mission/op and at this point he is withholding what could be vital information for unknown and likely personal reasons. It is pretty much screaming "I don't actually trust you or think you are competent enough to do this." which would piss anyone off. I wonder if he would be doing the same if it was Carl (Carlo? I really wish they would stop swapping it).