Saying "bye, bye, plane," repeatedly does not qualify as bad behavior. The fact that he wasn't screaming and crying from exhaustion after an 11-hour delay tells me that as a parent she did her job well to keep him calm and comfortable.
After being delayed for 11 hours, most children (and adults) would be irritable, to say the least. I would rather hear a child say, "Bye, bye, plane," over and over again than have to listen to some boring guy drone on and on about his career while I'm trying to sleep in the next seat.
As long as the airline is selling seats to parents and children, you're going to have to fly with them. Deal with it. It's not like the kid was running up and down the aisles. If you don't like to listen to children's voices, take a private plane. Airlines are the public transportation of the skies - I made the decision not to fly anymore because I don't like that sardine-in-a-can feeling. You can make the same choice.
The mother remarking that she would not drug him just so the FA could have a pleasant flight makes me wonder who else she would have said that to and what else wouldn’t she do...
If anyone ever suggested that I drug my child, my reaction would not be so calm. My response would be: "You sold me the seat. You said my child could fly. And then the flight was delayed 11 hours. And you want me to drug my child?! Since when are flight attendants qualified as doctors?" You don't know what kind of reaction a child will have to a medication.
Not one passenger complained. Only the flight attendant had an issue. If she can't handle stress on the job, she should get another job.
There is more about the passengers sticking up for the mom in the article at the link. I think the pilot was a little foolish to put this woman and her child off the plane too. Nobody corroborated the flight attendant’s story about being threatened.
http://www.11alive.com/news/article_news.aspx?storyid=99986