I'm gonna do my best to win. I read him the statute defining a bicycle. It said all that is needed to tell the cop,...
You made a huge mistake. The place to argue your case is not on the side of the road, but in front of the judge.
By trying to "educate" the cop at the scene, you basically telegraphed your whole argument and allowed the cop to not only try and come up with a better ticket with absolutely no mistakes, you also tipped him off to your planned defense so he can be better prepared in court. Plus, now that you've made a huge deal about what should have been a simple ticket, he's going to make notes about every aspect of the incident that he can use at trial. Cases like this are won or lost on the details, so the fewer details the cop can testify about helps you out tremendously.
A much better approach would have been to let the cop write a simple "riding a moped without a license" ticket. Then, when he shows up in court expecting only to testify on the fact that you didn't have a license, you blindside him with all the legal definitions in the statutes and contradictory laws. He'll be caught off guard and unprepared, and you'll steamroller right over him in front of the judge, easily winning your case.
People have to learn when dealing with law enforcement, whether it's a traffic ticket or a felony, just keep your mouth shut and let the cop take all the shortcuts and make all the mistakes he wants to, and worry about pleading your case later in court. You'll have a much better chance of winning. Any information you give the cop at the scene will absolutely not help you at all. It will only hurt you.