I would argue that the way in which Shakespeare manages to capture universal elements of being human in his plays make them worthy of study for all of us. The way he depicts the challenges that face true love, for example, or the experience of betrayal, grief and desolation help us to understand what it is to be human so much more clearly.
Leo Tolstoy derided "A Midsummer’s Night’s Dream" as "the most insipid ridiculous play that ever I saw in my life."
Voltaire called the Bard's oeuvre an "enormous dunghill." In a 1944 letter, J.R.R. Tolkien dismissed reading and analyzing Shakespeare’s works as “folly." Plenty of great writers were not fans (which some might argue is due to "the green-eyed monster").
"Shakespeare’s ability to summarize the range of human emotions in simple yet profoundly eloquent verse is perhaps the greatest reason for his enduring popularity. If you cannot find words to express how you feel about love or music or growing older, Shakespeare can speak for you. No author in the Western world has penned more beloved passages."
The Daily Dot noted that many people find Shakespeare "unreliable and out of date."
Not liking Shakespeare doesn’t make someone a philistine, especially if people want to talk about why Shakespeare doesn’t work for them. Why should a writer be exempt from criticism just because his works have managed to survive for centuries?
If you speak English, you've been influenced by Shakespeare. Bernard Levin has a famous passage that illustrates this phenomenon:
If your lost property has vanished into thin air, you are quoting Shakespeare; if you have ever refused to budge an inch or suffered from green-eyed jealousy, if you have played fast and loose, if you have been tongue-tied, a tower of strength, hoodwinked or in a pickle, if you have knitted your brows, made a virtue of necessity, insisted on fair play, slept not one wink, stood on ceremony, danced attendance (on your lord and master), laughed yourself into stitches, had short shrift, cold comfort or too much of a good thing, if you have seen better days or lived in a fool's paradise - why, be that as it may, the more fool you, for it is a foregone conclusion that you are (as good luck would have it) quoting Shakespeare.
Shakespeare invented over 2,000 commonly used words, such as "amazement," "luggage," "gossip," "bump," and "eyeball."