Primarily, trust. PuTTY is a security product, and as such it is particularly important to guard the code and the web site against unauthorised modifications which might introduce subtle security flaws. Therefore, we prefer that the Git repository, web site and FTP site remain where they are, under the direct control of system administrators we know and trust personally.
Large organisations seem less trustworthy to us because they have a lot of employees, any of whom could attempt an insider attack; because management can change or companies can be bought out, and a benign company today could become a malicious one tomorrow.
Github in particular already seems like a dangerously large single point of failure. I'd rather contribute to the Internet being distributed than contribute to it being centralised. In addition, the Github software isn't itself free, so although you can export the actual source repository itself at any time (every ‘git clone’ does that), you're locked in once all your other metadata (issues, pull requests etc) is stored in Github's format on Github's systems.
I know that if you have a Github presence already, it would be most convenient for you if everyone else was on Github too so that you could interact with them all in the same easy way. Sorry about that. But that seductive ease of use is how large companies attract a large user base to monetise or exploit later, and we don't want to participate in that any more than we have to.