I'm with those that say your guitarist is half right. Your abilities WILL improve if you push yourself to learn some challenging songs.
At the same time, it's asinine to say that you "shouldn't" learn a song "because it's easy." Lots of great songs are easy. Audiences love them, and music is, after all, a performing art.
Also, it's one thing to say that you ought to work on something that's going to push your abilities, and another to say you "have" to learn a song that is way beyond what you're ready for right now. You'll just get yourself frustrated and probably mess up your technique more than you improve it. La Villa Strangiato would probably be stupid to take on at the moment. But there's probably something else that would push you but that's doable for where your skills are right now.
The thing to do is to divide your practice time between different goals; some woodshedding and exercises for sheer technique; some songs that your band is actually going to play, or might, and that audiences would be into; and a tune or two that you're doing just for the exercise of mastering them and stretching yourself.