Men often see religion in militaristic tones, whereas women see it more in terms of relationships. Neither is wrong, just different. Men will practice their faith in terms of fighting a battle: a battle against temptation, against the world, against the devil and his fallen angels. Women, on the other hand, often practice a more relationship-based spirituality. They practice their faith out of devotion to their beloved, Jesus Christ.
(As an aside, this is why the modern, one-sided emphasis on Christianity as a relationship is damaging. I don’t think it’s a coincidence that we’ve seen so many men leave the practice of the faith at a time when we only focus on the relationship aspects of following Christ.)
Another problem with altar girls is that service at the altar is supposed to dispose boys to the priesthood. It’s not that every altar boy will be a priest, but priests often come from altar boys. Allowing girls to serve at the altar while not allowing them to be priests is cruel, to be frank. It’s like letting a kid practice with a team, but then not allowing him to play in the game. Of course, some think the answer is to allow women priests, but Our Lord already precluded that possibility.
When girls serve at the altar, we make that service no longer about training for the priesthood; it’s simply another profane activity, like sweeping the church after Mass. Such an activity is an important service, but it’s not sacred, as the priesthood and service at the altar are supposed to be. Some might complain that the Church therefore thinks men are more sacred than women. Yet sacred duties are not about the person performing it, but about God who is being served. A proscription against girls serving at the altar was never a statement about the worthiness of girls, just as the fact that men can’t join a Carmelite convent doesn’t mean they aren’t worthy enough to follow St. Theresa of Avila. Likewise, the Blessed Mother isn’t “less sacred” than the Apostles just because she wasn’t chosen as one of the Twelve by the Lord (quite the contrary, in fact).
Further, having girls at the altar restricts the ability of the priest to really open up about life as a priest. If he has a mixed-sex gathering of altar servers, how can he talk about the priesthood without being insensitive to those who can never become priests? However, if there are only boys, he can reveal to them more openly what it means to be a priest.
Finally, allowing girls to serve at the altar removes a shield in the battle against today’s secular gender nonsense. Many Catholics who understand the problems with radical feminism don’t grasp that having no gender distinctions in the Church (other than the priesthood) is a surrender to that radical feminism. If Catholics were to see a clear gender delineation every Sunday at Mass, they would be less likely to succumb to arguments that men and woman are the same. They will understand, subconsciously at least, that they are not. Often times having mixed genders on the Altar can create a distraction for those serving.