Passenger refused to give up his seat to an elderly woman: should he feel bad?

A young passenger refused to give up his seat to an elderly woman, claiming that she had no more rights to the seat than he did. The airline's client was flying on a long international flight and settled into the aisle seat he had chosen when booking to "stretch out easily" and have access to the restroom.
"When a woman who was in her 50s and spoke little English sat down next to me, she politely asked if I would like to take her middle seat, and I declined," the man explained on Reddit. "Another woman, who spoke her language, sitting next to her, said it was uncomfortable for a woman to sit between two men," the Mirror website writes.
The passenger felt that while he sympathized with her, it was not a good enough reason to accept a middle seat on a long flight when he was already sitting in a better seat.
"We sat in our seats, and when I went to the restroom a few hours later, the woman sitting in the middle was talking to the stewardess. Then the stewardess asked me if I wanted to move because she had a headache and was uncomfortable, and the flight was overcrowded," he continues. - "I was uncomfortable, because I'm a young guy who refuses to give up his seat to an older woman, but I said it was a hard request and I couldn't accept uncomfortable conditions.
In the end, the situation was resolved by a kind stranger who suggested that the young man give up his seat and then switch with the woman for her middle seat.
"The whole experience made me wonder if there wasn't a better way to accommodate this woman's request instead of pressuring me, or offering me incentives to switch, or making an announcement on the loudspeaker looking for volunteers, or something else I hadn't thought of," summarized the passenger who was the first to be in this situation.
In the comments below, opinions were divided on whether he was right to refuse the transplant.
One person supported him, arguing: "She could have paid for an aisle seat if she had a problem with that seat, because there's a 50% chance a man will sit you down. I would not have moved because there is a simple solution. People just want it to be free."
Others were more sympathetic to the woman's situation, with one commenter writing: "Although the assumption is that she was trying to save money, I believe she was not familiar with flying. Perhaps she would have been more than happy to pay for a seat if she knew how it worked, or as speculated, perhaps it was a last minute booking when there were no other accommodation options available.