Shaw was a terrible person with incredible powers who had done a lot of bad things. Why was it so bad that Magneto wanted to kill him, even out of revenge? Why did that issue have to be such a relationship-divider between Magneto and Xavier?
The dialogue in question (thanks IMDb):
Professor Charles Xavier: Shaw's declared war on mankind on all of us, he has to be stopped.
Erik Lehnsherr: I am not gonna stop Shaw, I am gonna kill him. Do you have it in you to allow that? [Erik pauses while Charles shifts in his chair uneasy]
Erik Lehnsherr: You known all along why I was here Charles, but things have changed. What started as a covert of mission, tomorrow mankind will know mutants exist. Shaw, us, they won't differentiate. They'll fear us. And that fear will turn to hatred.
Professor Charles Xavier: Not if we stop a war, not if we can prevent Shaw, not if we risk our lives doing so.
Erik Lehnsherr: Would they do the same for us?
Professor Charles Xavier: We have it in us to be the better man.
Erik Lehnsherr: We already are! We are the next stage of human evolution, you said it yourself...
Professor Charles Xavier: [cuts in] No, no...
Erik Lehnsherr: Are you really so naive as to think that they won't battle their own extinction? Or is it arrogance?
Professor Charles Xavier: [looks at Erik in disagreement] I am sorry.
Erik Lehnsherr: After tomorrow, they are gonna turn on us. But you are blinded because you believe they are all like Moira.
Professor Charles Xavier: And you believe they are all like Shaw. [leans forward]
Professor Charles Xavier: Listen to me very carefully, my friend: killing Shaw will not bring you peace.
Erik Lehnsherr: Peace was never an option.
I'm not sure how the movie could have made it any more clear. Xavier is on the path wanting to forge peace and understanding between mutants and humans. Magneto believes peace is not an option.
Killing Shaw cements Magneto's position: it demonstrates that Professor X's and Magneto's philosophies are irreconcilable.