Chemical Damage-- I think it's interesting that we are less concerned with "pool chemicals" when we talk about swimwear. We seem to discount the fact that any "pool chemical" that causes "chemical damage" to synthetic swimsuits might also be damaging to the biological fibers making up human hair and skin. But, it's the same fundamental problem. And we should remember that we get into the pool with our swimwear, so we are exposed to the same chemical damage.
Chlorine is a strong oxidant. (Think Clorox). Chlorine reacts with the chemicals that make up both synthetic (e.g., Lycra) and natural (e.g., hair and skin) fibers. In reacting with the fibers, the chlorine bonds to your suit, hair, and skin. It doesn't simply wash away in the shower, which is why the chlorine odor persists. That lingering, malignant chlorine continues to eat away at the fibers long after you leave the pool. In the case of your swimwear, it eats up the lycra, making it see-through and thin. In the case of your hair and skin . . . the dry, brittle, damaged fibers have names to themselves, such as "swimmers hair" and "chlorine burn."