Homebrew sometimes takes a while to get new erlang releases available. I seem to recall a release about a year ago that took over a month to become available. Something about other apps in homebrew that use erlang having to update before the homebrew erlang could be released, or something like that, I don't recall the details.

At any rate I've been using asdf https://github.com/asdf-vm/asdf to manage my erlang and elixir installs on a per project basis for a while now and it has been working well for me.