The Torah holds clothing in the same high regard, as the Written dictates every detail of what the High Priest will wear, and the Oral specifies how to fulfill the commandment of laying tefillin. Tradition tells us that the Israelites were on the lowest possible spiritual level when they were freed from bondage. One of the things that preserved their identity and prevented them from being a lost cause altogether was maintaining a difference in dress from the Egyptians. This is why many groups of Orthodox Jews choose to dress in a very distinctive manner today. Beyond appearances, however, I think Judaism requires a different approach to what we wear, and it is the reason I see no need to wear tefillin.
In the secular world, there is a lot of imitation in terms of fashion that goes on. Confusing style with status, people buy designer "knockoffs." When women began entering the work force in the 70s and 80s, they did so in "power suits" to prove they were up to the task. Rather than explore and express one's own unique potential, an individual mistakenly equates fashion with expensive, or success with masculinity, and seeks a quick, external fix to what they want to be.
The Jewish people are commanded to be a nation of priests. It would be a mistake to think that this is accomplished simply by dressing like the Kohen Gadol, whose role is undoubtedly important. One of the many groundbreaking advances of Judaism was the idea that each person could have a relationship with G-d without an intermediary. In short, the role of priest is not reduced to a garment. Clothing in Judaism is rife with meaning, and on many occasions, it points to something bigger than the tangible element. In other words, performing a ritual such as tefillin provides a way to capture the essence of inscribing the Torah on one's mind and heart, much like a picture book helps a child to follow a story.
I do not say this to emasculate men. I adore men. But it is no secret in Judaism that women are considered spiritually superior. Therefore, any mitzvah that men are held to must be understood as a step they are taking in an attempt to reach women's level. For women to imitate that step is not only superfluous, it diminishes our power.
I did not come to the decision to be Modern Orthodox lightly. I knew that I would face more temptation and have to constantly be on guard against secular influences. This is where the different approach to clothing comes in: Contrary to what the outside world says, in Judaism, what we don't wear is just as significant as what we do. I don't begrudge men their tzitzit, tefillin, kippot, or anything else that sort of beats them over the head with "Please TRY to behave more like the women and less like the animals, mmmk?" My exemption from wearing any of these speaks to my ability to just get it naturally. When, that is, I fully own my strengths as a woman and take my cues from Jewish tradition, not secularism.
In Judaism, we don't imitate; we innovate. If you are looking to grow as a Jewish woman, use the gift of your binah to love the Lord your G-d in everything you do, and lead the Jewish people--and the world--forward.