You have it backwards, the main garage opener is doing the learning, the cars button is just transmitting a signal. Doing this process, you’re telling your garage door opener “hear this new remote? Please allow him to open the door as well.” Presumably the car side buttons just cycle through a few common protocols (realistically there’s only 4-5 ones in common use, almost all garage door openers I the U.S. are made by Chaimberlain/Liftmaster or Genie).
Actually I take it back, there might be learning on the car side as well, where you press a button on an existing remote, but all that does is tell the car “Oh, this is a Chamberlain SecurityPlus 1.0 remote, I’ll start acting like one of those.” The actual rolling code and security algorithm is never decoded/cloned on the car side.
