There are many problems where a GC is too intrusive (one notable one is: writing a GC). Until you acknowledge this, Rust will make little sense to you (nor will C or C++, for that matter).

The whole problem Rust is trying to solve is that a programmer can do manual memory management without anyone needing to trust that they have gotten it right. The compiler can automatically check correctness (except for unsafe blocks, which are kept to a minimum).