Music has far more power than most of us realize. I'm sure you've noticed how profound an effect music can have on your mood. In truth, its effects reach even deeper.
There are two issues regarding non-Jewish music: the lyrics, and the music itself. Maimonides, a noted medieval codifier of Jewish law, discusses the issue of lyrics. If the content of a song is either heretical, immodest, or in some way negates Jewish values, it may not be listened to. This is the halachic perspective.
On a more Kabbalistic plane, the fifth Lubavitcher Rebbe explains that a composer of music invests his or her very self into the work. The music is an expression of the composer's soul, and listening to music connects the listener's soul to that of the composer. In light of this, do you really want to give yourself a soul-connection to just anyone? Especially if the composer is an individual whose spirituality and values are suspect at best?
There's another interesting point about listening to non-Jewish music. Following the destruction of the Holy Temple, listening to music was prohibited as a sign of mourning. It only became permissible again due to its profound ability to inspire people in their service of G‑d. After all, that is music's ultimate purpose.
Click here to see a few articles on the effects of music as well as its place in Judaism.
Malkie Janowski for Chabad.org
Secondly, we see that goyishe pop music comes and goes in popularity within about a decade whereas classical music is still lingering for 100's of years later. Meaning to say that these goyim invested so much so of their goyishe souls into their music that made it perpetuated until this very day. So thereby for a Jew to hear this type of music would result in them drinking from such a deep tamey goyishe source of a soul Chas Vesholom.