If your entire argument is based around stuff you've seen in movies, I don't think it's going to be terribly convincing.

There's no guarantee, a gangster could just follow you to wherever you moved, or could say "you don't have to pay" and come by the next day and break your legs. Or they could show up without notice and demand that you pay twice what everyone else does. Because extortion is illegal, so it doesn't follow any rules.

Here's some obvious differences:

• No one has any say about whether extortion exists, who gets targeted or how much anyone pays.
• Everyone gets equal representation in government, and tax laws do change because people advocate for it.
• "Protection" in terms of extortion just means they'll stop threatening you with force. It's not actual insurance or additional policing or anything like that. The only benefit to extortion is that the threat is delayed.
• Government provides actual protection, in addition to providing the means for exchange, and the infrastructure that allows for the transactions to occur.
• Extortion isn't predictable. Maybe the police will put the people in jail? Maybe a different criminal will decide to extort you as well. Maybe they'll feel bad for you and not bust up your shop this week? Maybe they'll charge double because they're in a bad mood. The amount is determined by whatever they feel like, and the penalty is almost always immediate with no due process or chance to argue your case.
• Taxes are passed by elected representatives in public and the rules that dictate what gets charged, when, to whom, when it's due, what your rights are if you disagree, or can't afford to pay are, are all public and all applied equally to everyone.

The fact that extortion and taxes both share two properties (the potential use of force, and the exchange of money) doesn't mean that they're the same thing.