There was once a funeral Mass in a Catholic Church for an individual who
was widely known and greatly loved throughout the larger community.
Many people were there, and the family of the deceased asked a
non-catholic to "sing a song" during the Mass. The priest was very
reluctant because the non-catholic had never been to a catholic Mass
before and so did not understand the nature of the Mass. After much
pressure he agreed to allow the song. Afterwards, he greatly regretted
his choice. The singer turned what was supposed to be a communion
hymn into an opportunity to draw attention to himself. This is not to
say that the singer did not have talent, he did; yet, he was not leading
other people to God, but to himself ("look at me, ain't I wonderful?").
What is singing for? Maybe it would help if I began by asking, "what is singing not for?" If we can eliminate some of those errors, then it would make it easier for us to consider what singing is actually for. Of course, we need to differentiate between singing in general and singing within a liturgy. These two situations are certainly not equivalent. How and what we might sing when we are driving down the road compared to what is done in Church should not follow the same rules.
For example, I have some very eclectic tastes when it comes to music; I do not like all music, but I do appreciate some very diverse musical styles. This does not mean that everything that I like to listen to is necessarily appropriate in all the same settings. During meals I like to listen to very soft ambient kinds of music (I have even read that it helps with digestion!). I do not, however, like that kind of music to be playing when I am driving--the absolute last thing I want when driving is to fall asleep. When driving, if I listen to music, I prefer some pretty heavy rock and roll; the tempo helps to keep me alert and focused on the road. As you might expect, I do not want heavy rock music playing when I am eating--not relaxing at all.
This is just a simple example of how different musical styles have different settings. There is another layer, however, to what we are dealing with here. It is not enough to say that certain styles of music have a proper location, for what I consider "proper" for one style of music might not be what anyone else would agree with (maybe someone likes soft music when they are driving so that they do not get stressed?). This means that we must realize the "personal taste" factor cannot be ignored. You see, we in modern society are so enamored with entertainment, that it is very difficult for us to distinguish between something that we like because it is personally enjoyable, and something we appreciate because it has a value that goes beyond ourselves.
What is the "value" of a certain musical style while driving (to continue to use this metaphor)? It will be determined largely on what the need of the situation is (which will not be the same for everyone). In asking this question, we must acknowledge that in the worship of God, it is not merely an issue of "taste" because we are not dealing with something that is allowed to be tailored to each individual's personal preference (contrary to the goofy antics that you see in some Catholic Masses!). There is only one goal that people are supposed to be aiming at when it comes to worship: personal humility and reverence toward Christ (which are two sides of the same coin).
Singing in the Mass in such a way that we draw attention to ourselves (as with the individual mentioned above) for the purpose of self-aggrandizement is a grave sin. Yet, drawing attention to yourself is just as self-serving as is singing merely because you enjoy the song. When the singing is not done to glorify God and assist those present in drawing closer to Him, then it is sinful. Just because someone enjoys a particular song does not mean that it is automatically glorifying God. Doing a "good job" does not guarantee that you are encouraging holiness. There are a number of musicians with great talent who are doing nothing to glorify God.
The purpose for music in the Mass is to do exactly as I have said above: lead the faithful to a deeper personal humility and reverence for God. This is why the Church says (yes, still today!) that Gregorian Chant always takes precedence in the Mass; all other forms are secondary. Pop music might be enjoyed, but it does little to deepen reverence. Singing because we enjoy the music is fine if we are singing at home, but that is not supposed to be our motivation for music in the Mass. So then, the question "why do we sing?" is easy to answer. "Why are you singing?" is the real question for us.