"My music is better than your music!"
More important, when such lists differ from our own, we can profit from the encounter by revisiting music, books, or whatever that we should reconsider, or by reading or listening to something new to us. When I was a Young Baroque Fascist, I thought, based on brief listens to his "sheets of sound," that John Coltrane was, if not quite a joke, at least a self-absorbed denizen of his own universe with nothing worthwhile to say to me. I had to learn a lot more about music before I could appreciate how Coltrane's music fits together. (I have even grown to respect Rahsaan Roland Kirk, though not to the extent of keeping his music in heavy rotation.)
Similarly, if a person's only exposure to Steely Dan has been their early hit "Reelin' in the Years," they should not be faulted for writing off the band. There is little in "Reelin' in the Years" to indicate that, in the fullness of time, the albums Aja and Gaucho would saunter into view.
Problems arise, however, when people take their own lists (or that of some authority; eg, a writer for the New York Times' list of "Top 10 Classical Composers") as establishing an absolute ranking rather than a personal preference. Just what does it mean to say that Beethoven is the "greatest" composer, ever? (It probably means only that anyone who says such a thing didn't get the memo that "Mahler is the new Beethoven.") Without a rigorous definition of greatest, people might as well save a lot of time and effort by just getting drunk and yelling at each other.
I have no problem with the idea that, in terms of having had the most significant impact on the course that Western music would take, Beethoven is the most influential composer. I also think that that is an inquiry that can stay within reasonably objective grounds. It was Beethoven and Beethoven alone who liberated Western art music from the need to rely on words to convey specific meanings. Even more important for the future of Western society as a whole, the specific meanings Beethoven most often conveyed were of the inestimable, God-given worth of every human being, and that institutions exist to serve people, not the other way around. It's a disservice and a willful blindness to separate Beethoven from either his revolutionary fervor or from his religious beliefs. But Beethoven's historical and social importance is one matter. That of "the greatest composer" is another.
If "greatest composer" means "he wrote the best music," a sane person can only respond, "Sez who?" If Frederic Delius's The Walk to the Paradise Garden, from A Village Romeo and Juliet, engages my emotions more strongly than does Beethoven's "Moonlight" sonata, that is my business and only my business. After all, I am the world's foremost authority on my own preferences.
I cheerfully admit that I, too, can be subject to the instinctive reaction that some music is "better" than others. But as a fair-minded person, I recognize that in trying to substantiate that proposition rigorously, I just end up looking foolish. It all boils down to variations on "Salvador Dalí must be a greater artist than Jackson Pollock, because Dalí's work shows exquisite draftsmanship not far removed from that of any renaissance master's, and a grasp of perspective achieved by no other 20th-century artist; whereas Pollock merely threw buckets of paint at a canvas on the floor." Of course, many people today find that there is more to be gotten out of Pollock's passionate best work than from Dalí's often-cold formalism.
As John Atkinson has observed, classical music excels at examining several complex, even contradictory ideas in great depth, while rock music excels at conveying one simple idea with great urgency. "Horses for courses" is an excellent phrase to keep on handespecially when people blow a gasket when your list of "The Five Greatest Composers" doesn't include you-know-who.