% ls -ld /usr/local
drwxr-xr-x 14 root wheel 448 Jun 10 07:14 /usr/local
% ls -ld /usr/local/*
drwxr-xr-x 105 root wheel 3360 Jun 12 10:32 /usr/local/bin
drwxr-xr-x 7 root wheel 224 Oct 30 2018 /usr/local/gfortran
drwxr-xr-x 12 root wheel 384 Jun 4 15:49 /usr/local/include
drwxr-xr-x 5 root wheel 160 Feb 21 2019 /usr/local/info
drwxr-xr-x 49 root wheel 1568 Jun 4 15:49 /usr/local/lib
drwxr-xr-x 2 root wheel 64 Jun 9 2019 /usr/local/libexec
drwxr-xr-x 3 root wheel 96 Feb 21 2019 /usr/local/man
drwxr-xr-x 9 root wheel 288 Jun 4 15:33 /usr/local/share
% mkdir /usr/local/opt
mkdir: /usr/local/opt/: Permission denied
I'm not using homebrew, so I don't know if there is something special about their/your configuration or something obsolete about mine ... but over the course of many versions of OSX/macOS, I've never been able to write to /usr/local without root ...
Eric