They don't. They're fairly orthogonal concepts. You can have a concept of lifetimes without memory management (for example, the object changes state while you have a reference to it).
It provides historical context. Someone coming from a gc langage that has never even had to learn what memory even is wrt to a program will not understand why a borrow checker is even a thing.
You can get very far writing software without even being aware that your language is even doing something called garbage collection for you, or without even having a basic concept of memory being tied to values, sizes, etc. If you lack this context a borrow checker just seems like a pointless nuisance.
If you are writing C or C++ and aren't thinking about ownership and lifetimes, you have either statically allocated everything or you are doing it wrong.