These phrases get tossed around a lot.  This is my belief:  Music is subjective.  So is greatness.  I think it is hilarious and kind of sad when I hear from someone something like the following:  "Igor Stravinsky (or substitute another classical composer's name as you wish) was the greatest composer of the 20th century (again feel free to substitute other centuries or use words like 'of all time')."

 

Keep in mind that there are genres of music.  Perhaps in the academic/Western classical idiom you could make such claims as "so and so is the greatest."  But the music world is so vast (and like the universe it is constantly expanding) that any attempt to quantify such qualitative, subjective, and feeling-driven creations is garbage.  And, no matter how much you think you know about music there's much more that you actually don't know about music.

 

So listen to what you love and maybe introduce others to some wonderful music you know; but open your heart to other musics as well.  Because chances are what you are into musically is only a speck of what's available in the music world.  So you might love classical, rock, jazz, etc.; and you're still talking about small wedges of a very big pie.  Finally, please put aside your arrogance and snobbishness.  It can be felt from afar;)