Homebrew install fails while copying files

I could get it working with

sudo chown -R $USER /usr/local

thanks to @joran for suggesting this in comments

You are getting permission denied when downloading the files into /usr/local.

This folder often belongs to root. This is a known issue with brew. Fix it by doing

sudo chown -R $(whoami) $(brew --prefix)/*

and then re-run the installer.