But if you think about Connie's position, you might hesitate a little

There's no way I would have let Carlo live. In a hypothetical setting if I had Michael Corleone's power, it would simply be an impossibility to let the man responsible for my brother's death escape swift and brutal retribution, regardless of him being my sister's husband. In addition to this, letting Carlo live would pose a direct threat to the family based on his treachery and his disrespect for the Corleones.

Since Michael chose to be Don, he had to kill Carlo. Even if he forgave Carlo's treachery personally, it would have shown him to have a "weak spot" that his foes would have exploited. And, as Tom explained to Kay (in the novel), "...treachery can never be forgiven...they [Tessio and Carlo] would have been a danger to all of us, all of our lives."

As Roth said, "This is the business we've chosen." Murder comes with the territory.