BtVS: Angel / Just do it for goodness sakes!

Buffy not taking her chances is likely to be a rule but I'll leave it as conjecture for now as this is an early piece of neglect on her part. There is no reason for Buffy to not kill (or try and kill) Angel, she barely knows him, she knows he's a vampire and there is fairly strong evidence to suggest that he has just fed on her mum. It's not sufficient to point out the fact that this evidence was wrong, Buffy slays often without examining the evidence thoroughly.

And how costly was this neglect in human lives?