Ok, this may get to be kind of long, but I'll keep it fairly simple. I, too, love modern literature and there are some awesome books out there. But I do think it is valuable to read the classics for several reasons:
First, like the classics, modern literature says a lot about our times. When you read the classics, you get a real sense of what life was like. True,
Red Badge of Courage is dry and dusty by comparison to
Cold Mountain, but it give a whole different view from a different time. Crane in 1895 looking inside a young soldier's head while that soldier is on the battlefield. If you want to see how people thought, what the world was like, etc. go to the classics of any period.
Secondly, the language of the classics is what mostly puts people off. It is very difficult in most cases. But here's the thing. Reading the classics demonstrably improves vocabulary. In
David Copperfield, for example, there are over 1100 "big words," SAT type words. So if for no other reason, self improvement is a reason to read the classics. Also, experiencing difficult, downright convoluted style is kind of like eating strange foods. You may not like olives, Feta cheese, samosas, fine wines (oh yes, you're too young for that), and all that stuff, but if you never allow yourself to take the challenge and try something, you'll find yourself eating burgers and American cheese, watching "feel good" movies, and reading only the easy stuff. Take a chance, work that brain! Hone those literary tastebuds.
Lastly, the stories and themes in the classics are relevant to us in many ways. Take
Frankenstein, for example. Difficult, convoluted style, big words, perhaps a little tortured and melodramatic, drenched in the sentiment of the early 1800s. OK. But it's really ABOUT the limits we should put on science. Should scientists be allowed by government or religion to explore everything, without restraint? It's also about parental responsibility. If you create someone (e.g. a child) are you responsible for its actions? Could your bad treatment or rejection of a child lead to that person's criminal behavior later, and if so, are you responsible? It's also about the creative process. If an author creates a "monster," a work so odd, so different, so in the face of convention, can that author be blamed for how the "monster" turns out? You see what I mean? Now those are interesting questions we might never ask if we never read anything old. People have thought of the same stuff that concerns us for many, many years.
So my advice to those suffering through turgid, old books in English class is look for the positive in them. No, I don't like all the classics and sometimes wonder how in the world they got included in the cannon of classic literature. That's fine. But I don't discount all old books. I work on the challenging stuff in small bits and read the cool, fun stuff along the side. The best of all possible worlds (no offense to Voltaire).