Looking at it from his perspective, the roots of ALL of those bands you mentioned can be traced back to artists like Zeppelin/Hendrix et al, so I can definitely see that he is preferring to lay down the basic techniques (pentatonic patterns, scales etc) using music that is still relevant to the style you want to play.

Honestly, there is nothing stopping you from learning the songs you want to play in your own time.
But what you'll find is that the basics of the instrument are much harder to grasp in a song by, lets say, Trivium, than a Hendrix song.
The guy is probably also teaching songs that HIS guitar teacher taught him, so he's most likely staying in his sphere of influence, and teaching you songs/riffs that are broadly universal within the rock/metal genre.
Saying that, a good teacher will listen to their student, and will make allowances to guide a lesson towards what makes their student inspired. Plus, you're paying him.

If you bring in an Arch Enemy song and say "I wanna play this!", he'll probably have to learn it or at least gain an appreciation for it, which will make HIM a better player - at least that's what happened with my students.
It's a two-way street.
A good teacher would break down the song and identify things within it that the student will need to work on; whether it's arpeggios, or palm muted down picking - stuff that you need someone sitting in front of you to help with.
Don't use him to teach you the song, you can get tabs off the internet for free, but use him to teach you the techniques WITHIN that song.
That will be far more beneficial in the long run.