Since this seems to be a bit hard for you to understand; let me build a strawman:
When you join the service, you are issued a uniform. You are not allowed to wear anything else in boot camp. If someone tells you that you CAN, you'll be in big trouble.
So when Sarge says, "Get rid of ANYTHING Unca Sam did not give you.", I'm sure you'll know EXACTLY what he is talking about!
Same idea applied when Paul says, "Don't teach that OTHER stuff."
Except there was no OTHER stuff in Christian communities north of Antioch until after Paul had been killed.
Antioch is where Simon Peter settled in. And other than the 'works & faith' vs. 'faith alone' conflict, Peter didn't have any doctrine that was at odds w/ Paul -- much less a doctrine that required a warning from Paul about corrupting the Church in Ephesus & Crete.
The 'false' doctrine was Gnosticism that showed up in the first part of the second century.
Paul could not have written I & II Timothy warning about false 'science' - 'knowledge' - 'gnosis'. Paul had died at least 35 years before.