Another fun fact: occasionally, that’s a legitimate technique. I have an old manual Toyota 4Runner 4x4 that actually has a “clutch start cancel” button you can use if, say, you stall in a tricky rock-crawling situation. You can crank the starter to crawl forward without risk of rolling backwards, like might happen if you actually started the engine and tried to use the clutch.
The key is to understand what the controls do instead of memorizing a procedure.
When you start the car, you probably don’t want it to instantly lurch forward. So, you need to decouple the engine from the wheels, which you can do either by putting the transmission in neutral or by pushing in the clutch (or both). Once it’s running, either you can let the clutch out in gear to start moving, or let it out in neutral if you want to remain stopped for a while.
It’s not so much that one procedure is “correct;” it’s that you decide what you want the car to do and manipulate the controls to make that happen. It’s only not correct if it does something you didn’t intend.