and best on his tone in what I read, I would bet that if he were flying without his kids and another A lister got on with kids ahead of him and took the seats he wanted (bulkhead, maybe) he would get pushy about that and how kids do not qualify to board.
Honestly, I can understand possibly not knowing or understanding the rule (but I doubt that was the case) or even just asking if they could board with him (politely asking), but when he was told "no" he should have left it at that and followed the rule he now knew.
I am still guessing that whatever was tweeted was much worse than he says and that is why it caught someone'S attention and he was told he needed to remove the threat.
Also, sometimes people who are borderline are removed from a flight and then spoken to and allowed back on (or allowed on a later flight). It is certainly possible that if the tone of his post was angry or threatening, security wanted to question him and ascertain his mental state before determining that he was not going to go off the deep end mid flight and was safe to allow back on.
I assume Southwest cannot violate his privacy by releasing the exact tweet or explaining further who made the call to remove him or why and why he was allowed back on--but I sure wish someone had caught the tweet and would contact the news.