Another point is after the initial situation with the agent he admits to blurting out "Twitter will be hearing about this!". Perhaps. you have a different life experience, but the folks I meet in life that use phrases and tactics like this are far from reasonable people. They are the "I'm taking my football and going home!" types, when they don't get to be quarterback. His children were too old to qualify for the Family Boarding policy SWA has which is after the A group but before the B group. He'd had to have paid more for his tickets to get his children in the A group with himself. He simply chose not to and was hoping to get his kids through with the higher paid tickets for free. He intentionally planned his trip poorly by either not buying the correct tickets he wanted, or going with an airline that would let him buy assigned seats.
A major issue is that he did not simply state "The agent for flight X was very rude, I'm dissappointed @SWA". He proceeded to give her name and location out. This is what he admitted to openly, and based on his previous behavior that he admitted to, I'm inclined to think it was worse than he said. She very well might have been nervous for her safety, you don't know her situation, and nobody has heard her side of things yet. She might have an abusive ex she is trying to avoid, etc. It was not his place to do that. She might have been wrong, but nobody knows for sure because nobody has heard her say anything. Visit this man's twitter. It's private now, but you can still see he styles himself as a social media buff. He knows exactly what he's doing. At least be fair to her and cast judgement later.