Everyone makes mistakes. Sometimes it's simple forgetfulness, sometimes it a misunderstanding, sometimes we're just oblivious to the effects of our actions because we are momentarily self-absorbed. In each of those cases, an apology is warranted.
The problem is... when you apologize to a leftist it's often demanded, never accepted and always taken as a sign of weakness. Why? Because that's how they think - if you get caught insulting someone - you don't apologize - you double down and make the insult worse. If you get caught in a lie; you don't apologize, you double down and tell a bigger lie. So, when you, the rational person, apologize whether demanded or not, you are signaling weakness and they will attack. Every time. Without fail.
This is true of all Bigoteers, whether they're a simple useful idiot university student, a community organizer, an academician, or an elitist such as you find in D.C. or Hollywood.
They're not actually interested in your apology - they're interested in using you to make a point - 'we have the power, you don't' And they do it all the while claiming victim status.
You can apologize to a Christian, or a libertarian, a conservative, or even a classic liberal, and it will probably be accepted in good faith Just don't waste your breath on the Bigoteers of the world.