When you focus on the outcome of your words, you will be careful not to insult others. Imagine the harm you are causing yourself by turning this person against you! Practically speaking, you never know when you will need this person’s help or friendship.
Of course, we should avoid hurting people with words because it’s the right thing to do. But at least we should do so out of enlightened self-interest!
Sources: see Vilna Gaon – Proverbs 11:12; Rabbi Zelig Pliskin – “Consulting the Wise”