What is Jesus really saying about oath swearing?

For Jesus to say that swearing an oath is wrong would go against the teaching of scripture. Swearing an oath in and of itself was not considered to be a bad thing under Old Testament teaching, and Paul himself swore an oath in the book of Romans.

Then why would Jesus be saying that we should not swear at all?

Is it possible that Jesus is talking about a certain kind of swearing? Or is it possible that there are some heart issues that Jesus is dealing with here? Or could Jesus be condemning religious game playing that involved adding to and subtracting from the Law while trampling on the original intent of the Law?

Actually, Jesus is talking about everything mentioned in the paragraph above.