There's a skill to learn in keeping engineering concerns to yourself. It's unsurprising when management or executives are faced with decisions in unfamiliar topics they err on the side of Nay. Your mistake is involving them at all.
Using git locally is a tool just like your code editor. There's no need to ask your boss about that.
Since you're the only developer it's mainly to make it easy to revert any mistakes and to have confidence in deleting useless stuff (that you can recover later).
I echo your ??. Sure you don't need a central repository to use git. What does that have to do with suggesting some git hosts that aren't cloud based?
I'm very comfortable with git at the command line, but I still think it's valuable to have a web interface. For instance, with a web GUI I'm able to share a link to a specific line or range in a file in a specific commit.
Typically if I need to do that I'm asking a question or requesting a change, and in that case I want there to be as few barriers as possible to increase the chances that the other person cooperates. Asking someone to clone/pull the repo, checkout a hash, and then view a line in a file is a much higher barrier than asking them to click a link.
I honestly enjoy the work when I know what's going on. We have a lot of unique problems to solve, and I have gotten positive changes made, as well as some really good weeks where I pounded out some good code, but other times it's slow, sad, and frustrating.