In the persuasive essay, you must defend your side of an argument. You are no longer merely showing, you are convincing.
The persuasive essay must choose a side, make a case for it, consider and refute alternative arguments, and prove to the undecided reader that the opinion it presents is the best one. You must be aware of other sides and be fair to them; dismissing them completely will weaken your own argument.
It is always best to take a side that you believe in, preferably with the most supporting evidence. It can often be educational to adopt a different position from what you might normally choose (debating requires this kind of flexibility).