What is irony? Is it ironic for someone who was mad about getting the silent treatment to give it?

Not really. It would be ironic if the person giving the silent treatment would suddenly be GETTING it from those to whom he was giving it.

For instance, a team of 5 people are supposed to work together to complete a school project within 1 hour. One person gets annoyed that his ideas weren't accepted by the other 4 people and walks away and sits by himself, ignoring his teammates completely. However, he knows that he must help in order to receive a grade on the project. So, with 15 minutes left, he tries to rejoin the team, but the other four completely ignore him and won't allow him to do any work. The 4 receive a passing grade and the 1 receives a failing grade.

That is irony.

Hypocritical

Irony is when you say something but you actually mean the exact opposite

and are just saying it as a joke ...

''Yes, I'd love to stick my head in a dead sheep''

Edit .. Hypocritical is more like saying things you don't mean ..

The hypocritical. Irony is when you expect one thing and a totally different thing happens. Like a prostitute living on St. Mary's Boulevard :)

The other word you are probably thinking of is contradiction, or hypocrite.