Dear Simple,
The contradiction is not in what people wear or think. As humans we do all kinds of inconsistencies. But clothing (as an object) is either meaningful to the wearer just by what it is. Or, it has meaning because it gives off an impression of the wearer. Our intelligence may deduce from the clothes, something about the person wearing the clothing. But that is nothing to do with the clothing itself.
Identifying with the clothing, is a later step. My disagreement is about making this step. I think it is pointless. Tzitzis have an intrinsic meaning. I wear them regardless of what others perceive. That could be true for my entire wardrobe, which for the almost all of it is meaningless. [Just something to wear.] There is no need for me to identify with my tzitzis. Or any other clothes. Maybe people do it because they are lacking something better.