Censoring Classical Music

We talked a lot about whether or not to "censor" what popular music we may bring into class by skipping songs that may be controversial or by using "clean" versions of songs. I was thinking about how we may or may not censor classical music for use in our music classes as well; for example, last night I briefly brought up my usage of the John Dowland song, "Come Again" in my 6th grade classes. I have used in this song in class, but have never discussed the deeper, controversial meaning behind the lyrics. Am I wrong? Should I not use this song if I don't discuss the deeper meaning? Is it always necessary to discuss social issues surrounding a song?