That's an interesting question. My first thought is that milk would dilute out the chlorine in your eye, which would be similar to just if you splashed a little water in your eye. Milk might feel nicer as it has proteins in it that might coat your eye and soothe the irritation. I also looked up some information on how chlorine irritates your eye, but I'm not entirely sure how reliable the scientific source is. Chlorine attacks your eye and adding milk adds more material for the chlorine to attack. So instead of attacking your tissues it attacks the proteins in milk. Other people have said that chlorine isn't really the culprit of skin and eye irritation, but rather the pH of the pool. If the pool pH is off it could irritate your eye. Milk is closer to a neutral pH and so could perhaps counteract the effects of the pool water. Whatever the answer is, it seems that many people suggest putting drops of milk in your eye to help with irritation after swimming in a pool.