Homebrew fails on MacOS Big Sur
I had the same problem. Try upgrading brew - this solved it for me.
I have solved my problem reinstalling brew with this script (install.sh):
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install.sh)"
Homebrew 3.0.1 Homebrew/homebrew-core (git revision 47e5d; last commit 2021-02-14)
Then just proceed with: xcode-select --install
You should update brew;