"I explained to her that it was a joke", he apologised.

This clipping on the right is from an article in the Guardian.

Recently, a footballer named Ada Hegerberg won a Ballon D'Or, which is a football award. She was asked if she knew how to twerk by the man presenting the award and apparently 'seemed to attempt to leave the stage, before reluctantly agreeing to dance to another song'.

The man, Martin Solveig, says that he apologised. Now then. An apology, I think, has to include the words 'I'm sorry' or 'I apologise' or something along those lines. To be effective, it also has to acknowledge that harm was done, and it has to apologise for the right thing. Let's see how he does.

'I explained to [Ada]'

Oh dear. Explaining to someone that they were wrong is not really the same as  apologising to them.

'My apologies to anyone'

Well, it's Ada who needs the apology, but I guess that includes her?

'who may have been offended'

Ah, OK, he's not apologising to her. If he was, he'd have apologised for making inappropriate comments or making her feel uncomfortable or overstepping his boundaries. He's apologising to the world at large who may have been offended. But maybe no one was offended! Maybe nothing was wrong at all! Maybe there was no need to apologise at all! In which case, it's a good thing he didn't.