I've argued before that Fredo was not a threat to Michael, was not believed by Michael to be a threat, and did not deserve to die.

This line ("He injured me.") is one of the reasons I've come to that conclusion. As you rightly point out, TB, it was a curious phrase to use in a confession.

But I do not believe that he is attempting to mitigate his guilt. Quite the opposite. I believe Michael's confession was genuine and that, for once, he is being totally candid. He is simply giving the true reason for why he killed Fredo - not that Fredo was a threat, but that Michael was hurt by him.

It was strictly personal, not business.