We'll have to agree to disagree. I believe that anyone should have the right to politely ask another passenger if they'd mind moving for whatever reason.
They can ask sure, but they don't have the right for the airline to try and talk the woman into moving on their behalf. He asked, she said no, which she had every right to. Funny how his first course of action though was to expect the woman to move, rather than solving the problem himself. If not sitting next to a woman is so important to him, why didn't he book an extra seat? There are ways to ensure he wasn't sitting by a woman, he chose not to do that. Why? Gee, i don't know, maybe he's just so entitled and misogynistic that he expects women to do whatever he demands.
That's not my beliefs but they have the right to their view, however much I don't agree, as long as they don't force it on anyone else. A request is not the same as enforcing anything. People are free to request, the same as others are free to say no.
But by demanding women move for them, they are forcing their beliefs on others. And the man didn't just request did he? The airline enforced his so called request for him by convincing the woman to move. They could have just said "the lady said no, there's nothing we can do." Instead they took his ridiculous request seriously. He has a right to his beliefs, he doesn't have the right to expect the rest of the world to fit into those beliefs.