(Disclaimer: the following are my own thoughts, and not the official reasons for TAC having the rules it does. I do not speak on the College's behalf.)
I think the characteristic quality of people my age is laziness. At this time of life, we have so much potential to do whatever we want with our lives. The main reason many people don't reach this potential is simply not being willing to work for it. Everything worthwhile must be worked for: if we were just handed all the good things of this life as children, what pleasure would we derive from them? This rule holds true for, I would argue, every aspect of life. What you achieve is directly proportional to the amount of effort you put into it. But the fact is that most people my age don't have a good work ethic and have no desire to work for what they want. This attitude leads to bad grades, slovenliness, carelessness about morals, and a host of other evils.
How, then, to fix this generational disorder? One way is to mandate effort. It sounds weird, but if you are required to put effort into something, it will get you used to doing so, even in non-compulsory situations. This is the beauty of the "fake it til you make it" philosophy. And that's one of the things that a strict dress code achieves. We have to put effort into a seemingly small aspect of life--the very clothes we wear--and as a consequence we find it less taxing to put effort into a more important thing, like our studies.
But that is only one of the benefits of having a dress code. Another is mindset. Like it or not, no one can deny that the mental disposition of a person while wearing sweatpants and fuzzy socks is not the same as the mental disposition of the same person wearing a business suit. Occasions for which we dress well tend to have more import, and thus we are more engaged in whatever we are doing. One thing our dress code has taught me is to take things more seriously. Dressing in such a way as to be better engaged helps us acknowledge the gravity of what we do in acquiring an education. At TAC, we place a great emphasis on education as a serious pursuit of the Truth. This pursuit is essential to education--how can we pretend to any kind of knowledge or wisdom if we are not constantly seeking out what is good, true, and beautiful? And if dressing well aids us in this search, we have little excuse to set it aside. As my friend Emily put it, our dress code is "our way of paying respect to what we set out to find in every class--the truth."
Another aspect of this discussion is paying attention to how we perceive ourselves and how others perceive us. As human beings, we depend on sense perception for our knowledge of the world around us, and sight is one of the principle senses we rely on. Because of this, we tend to make judgments about things and people based on appearance. This is not altogether good, but is also not necessarily a failing; someone's character is often manifested in their mannerisms, body language, and personal attire choices. It can often be an identifying feature--think of how easy it is to spot American tourists in foreign countries because of our distinctive habits of dress and mannerisms. It is a gift to have such an impactful way of expressing ourselves in our appearance, but it is one that ought to be used properly, as with all gifts. And it should be noted that this can sometimes work in the other direction, too: dressing better may positively affect my self-image.
If my dress can have this much weight for my perceived person--and perhaps in who I really am, to a certain extent--then I ought to take my habits of dress seriously. If I want to be construed as a classy, put-together person, worthy of respect, then I should dress in a classy, put-together manner that is worthy of respect. Every human being has inherent dignity as a child of God, and we should dress in accordance with that dignity. Dressing well serves as a reminder, to ourselves and to others, of our value and our right to be respected.
All this is common sense, and is reflected in TAC's custom of dressing with modesty and some degree of formality in classroom and social settings. Living with this custom has made me more aware of the dignity of myself and others, and of the importance of my education. Yes, it can be a pain at times, but it is well worth it.