Like others have suggested, use git locally, there's no need for them to be involved or aware of that detail. Do you consult them on what text editor to use?
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).
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.