So I have read this - https://wiki.archlinux.org/index.php/Python
And it is clear from this wiki that I can install Python 2.7.2 via
pacman -S pytho
Most unices already have a /usr/bin/python. Overwriting that one is a bad idea, as this is the Python version used by all packages in the system, and changing that one may break them. When installing the Python 2.7 package the executable should be installed as /usr/bin/python2.7 (if not I would claim Archlinux is broken) and it's better to use that when you want to run Python 2.7.
Archlinux is a bit special, since it will use /usr/bin/python for Python 3, despite the default executable name for Python 3 being /usr/bin/python3. This is confusing and can be seen as a bug, but it does mean you can't use that symlink for Python 2, as any other Archlinux script that uses Python 3 will almost certainly break if you do.
So where on other Unices, symlinking /usr/bin/python to Python 2.7 is a bad idea, on Archlinux it is a terrible idea. Instead just install all version you need and call them with /usr/bin/pythonX.X.