That teahcer of yours definitely isn't no video game fan if he doesn't think there's any good storylines in games.
Metal Gear Solid 3! (Or even the MGS series): There was so many twist and turns in that game I didn't think my heart could keep up, there was such a sad ending I nearly started bawling. IMO MGS3 storyline beats pretty well any movie I watched.
Also the Final Fantasy VII series. Especially FFVII and FFVII: Crisis Core. Again with FFVII there was so many twist and turns that I nearly took a heart attack. And also with Crisis Core it had one of the saddest endings to any video game I've ever played.
Other games with good storylines:
God of War
Zelda: A Link to the Past
Most Final Fantasy games
Assassin's Creed
Resistance (After playing 2 I have to get 3!)
Uncharted had an interesting storyline
Shadow of the Colossus has a very different storyline to most games.
