You can use pyenv to install python with:

brew install pyenv
pyenv install 2.7.18

Optionally set it to your global default:

pyenv global 2.7.18

Nice article on why using pyenv is better than using brew to manage your python installation.

To make python binary available globally, add shims to PATH:

PATH=$(pyenv root)/shims:$PATH

You can get any Python release, including the last Python 2, from the official download site:

https://www.python.org/downloads/release/python-2718/ → macOS 64-bit installer

The Python Release Python 2.7.18 | Python.org download page has a macOS 64-bit installer download that replaces the missing interpreter.

Homebrew doesn't do this, I would recommend using homebrew to install pyenv and then using pyenv to install and use python 2.7.10, and any other versions you need.

Get pyenv:

brew update
brew install pyenv

Then add eval "$(pyenv init -)" to your .bash_profile and relaunch terminal.

Install python 2.7.10:

pyenv install 2.7.10

You can then set 2.7.10 as the global python by using pyenv global 2.7.10 but I would instead recommend you look at the pyenv virtualenv or pyenv virtualenvwrapper projects and use a python virtual environment for your code, or set the python for your project folder only by cd'ing to your project folder and using pyenv local 2.7.10.

Please read the info printed by brew info python. It also links to the Homebrew website on Python, where it says:

The executables are organized as follows so that Python 2 and Python 3 can both be installed without conflict:

• 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.
• pip3 points to Homebrew’s Python 3.x’s pip (if installed)
• pip and pip2 point to Homebrew’s Python 2.7.x’s pip (if installed)

Apparently you have installed both Python 2 and 3 through Hombrew. If you wish for python to point to Python 3 (instead of 2.7), you have to put /usr/local/opt/python/libexec/bin in your PATH before other entries.

I have done this sort of thing in two ways - however both do not coexist with homebrew although I suspect there should be a way similar to the macports one.

General package manager

The first is using Macports as the package manager. There are separate ports for several python versions 2.x and 3.x currently 2.4, 2.5, 2.6, 2.7 and 3.1, 3.2, 3.3 3.4 and 3.5. For example to install 3.4 do sudo port install python34 There is also a python_select port that running it allows you to choose which version of python is run by /opt/bin/python. e,g, to select macports python 2.7 port select --set python python27

Each package manager needs to run as the only package manager otherwise it will be confused with unexpected different versions of libraries and executables on its paths.

From comments the similar homebrew way is given in https://stackoverflow.com/a/4158763/151019 Short answer seems to be brew switch the equivalent to port_select

Python version managers

The other way is install direct from python.org This will install a python into /usr/local/bin I think this installs a python and python3 executable. The issue with Homebrew is that it assumes that things in /usr/local are installed by it and so brew doctor will report these python.org pythons and libraries as issues and as this question shows also the frameworks in /Library will be problematic.

EDIT 8/2018 *** I would now suggest using conda either miniconda or anaconda. This is another package manager but based and mainly meant for python, it also gives the equivalent of python's virtual environments and pyenv (as per other answer) and so each project can be in a different python and different libraries (Macports only switches python version for all projects)