brew-installed Python not overriding system python

TL;DR Add the following to your .bash_profile (or equivalent):

export PATH="/usr/local/opt/python/libexec/bin:$PATH"

Explanation

It seems python via homebrew is now handled differently (see https://docs.brew.sh/Homebrew-and-Python).

• python3 points to Homebrew’s Python 3.x (if installed)
• python2 points to Homebrew’s Python 2.7.x (if installed)
• python points to Homebrew’s Python 2.7.x (if installed) otherwise the macOS system Python. Check out brew info python if you wish to add Homebrew’s 3.x python to your PATH.

Checking out brew info python hints at what you need to do:

Unversioned symlinks python, python-config, pip etc. pointing to python3, python3-config, pip3 etc., respectively, have been installed into /usr/local/opt/python/libexec/bin

The hint being that you therefore have to add /usr/local/opt/python/libexec/bin before /usr/bin in your path (not /usr/local/bin as stated in some sources e.g. https://docs.python-guide.org/starting/install3/osx/)

See also https://github.com/Homebrew/homebrew-core/issues/15746

One-liner to get homebrew python working:

zsh

echo -n 'export PATH="/usr/local/opt/python/libexec/bin:$PATH"' >> ~/.zshrc && source ~/.zshrc

bash

echo -n 'export PATH="/usr/local/opt/python/libexec/bin:$PATH"' >> ~/.bashrc && source ~/.bashrc

Explanation:
>> filename appends at the end of the file
source filename reloads the file