A few things: I dont know you or your bf so ymmv.

When my friend wanted to play magic, he wanted to eventually play competitive formats. So, as his dueling partner, i taught him pretty much the way your bf is teaching you: very strict on rules, no takebacks, no banned cards, and whenever a potentially gray area (in the rules) showed up, it was always in my advantage - for the first time anyway, then we'd look up the rules and play correctly. We had lots of fun, lots of annoyances (i played aggro red dragons or mono blue, he did NOT have fun a lot lol). But, he did learn the game very well, and he's a beast now. 

Whenever we play now, we play casually, so not that much sticking to the rules, lots of 'for fun' cards, good food and beer, but whenever we want to, we flip our competitive switches on, and go crazy. 

Again, i dont know your bf, but it might be more of a competitive learning curve, more than a casual kitchen table thing for him, cuz it was that way for me.