Mostly because Google built its own tools long before GitHub existed, and they were designed for a very different scale. Google keeps most of its internal code in one enormous monorepo, with its own version control system (Piper) and code review tool (Critique). Engineers at Google have described the reasoning in a 2016 Communications of the ACM article by Rachel Potvin and Josh Levenberg, 'Why Google Stores Billions of Lines of Code in a Single Repository.' Their argument is that one shared codebase makes it easier to reuse code, make company-wide changes and see who depends on what. A typical GitHub setup, with many separate repositories, doesn't fit that model well.
Google has also run public code hosting before. Google Code Project Hosting was shut down in the 2010s, and GitHub's dominance for open-source work came after that. Today Google hosts many of its public projects on GitHub, such as parts of Kubernetes and Angular, while still using its own internal systems for most of its work. Its engineers also helped create Gerrit, a code review tool that Android and Chrome have used.
So the short answer is that Google's internal system grew out of its own scale and history, and it already does what its engineers need. Building a public GitHub clone would be a separate product decision, and Google has generally chosen to work with GitHub's platform for open source rather than compete with it.
A
Is Gerrit open-source software?
Yes. Gerrit is open-source software, licensed under the Apache License 2.0. Its own project site and its official repository both say so, and it's free to download and run yourself.
It began inside Google. Wikipedia lists Google as its original author, and it's a fork of Rietveld, the code review tool Google released as open source in 2008. Its first independent release came in 2009. It's a Git-based review system, and the project is now maintained by a community of contributors rather than by Google alone.
One detail to keep in mind: the GitHub repository for Gerrit is marked as a read-only mirror, and the project asks for contributions on its own Gerrit server instead, so you won't submit changes there.
It's the same pattern as the earlier answer: Google's own tool, released openly, that other teams run on their own servers.
