Is William Shakespeare relevant to us?

As time goes by, more and more people claim that Shakespeare is not relevant to modern society, and that although his plays continue to be enjoyed by audiences worldwide, they shouldn't be taught in the classroom. This question asks for your opinion, but mine is a resounding YES! 

First, Shakespeare's characters are human, they're real people with real problems, who don't always act or behave in the proper way. His plays are timeless..... the star-crossed lovers, the ambitious, prejudice, discrimination, murder, fantasy...... and so forth. 

Many people complain about the impossibility of deciphering Elizabethan language, but I've never had a student who wasn't able to move past the language and see the words. In fact, many of Shakepeare's words and phrases are displayed and quoted all the time, often in advertising. An abundance of his phrases have even become a part of our everyday language;

"Green-eyed monster"

"In a pickle"

"The world is your oyster"

"It's all Greek to me"

"Catch a cold"

"Love is blind"

"Wild-goose chase"

"Heart of gold"

"break the ice"

"Laughing stck"

All of the above quotes have become a part of our daily language..... and they all originated with Shakespeare. Do you think his words are still relevant?