Linux ran fine on 386 chips - that was actually what it was originally developed on. But Intel added a bunch of functionality in the 486, Pentium, and Pentium Pro chips. At some point the powers that be didn't see any value in continuing to support pre-P6 chips anymore.

It was a bit of a strange decision since there were undoubtedly more 386, 486, and Pentium users than some of the platforms Linux continued to support, but that's the choice they made. But they weren't alone. Even NetBSD requires a 486DX or better.