Expostulation is an expression of protest, not a rant exactly, but often lengthy. If you have parents, you might be more familiar with the term "lecture," an expostulation on why you should never do the things you actually want to do.
If you've done any geometry proofs, you know that postulate means to put forward an assumption. Expostulate means to take that assumption away. For instance you might postulate that it's a good idea for you and your friends to drive to the beach in the middle of the night, but your parents might expostulate that it's not safe.