I've never taken a lesson (for my sins) but some years ago I did give a few lessons. I had both a second amp and a spare bass (as well as a few other spare bits and pieces) to make sure if someone turned up with equipment that was, shall we say, below par, then they'd at least have a half decent set up to use during the lesson.
I'd also take a guess that the chap you're speaking to probably isn't great at standard notation hence trying to push you into tab.
Honestly, I'd say find someone that can give you the kind of lesson you want, it sounds potentially like this chap won't fulfil your learning needs.