Sea water has literally hundreds of salts in considerable amounts, a number of them toxic (I think that KCl might be one of them). I seem to recall that when your body tries to get rid of these toxins through the kidneys, etc., you end up losing more water than you take in.
Your body attempts to maintain its tonicity–the total concentration of salt inside it. If you ingest a lot of salt, you require more water in which to dissolve that salt. Since sea water is hypertonic (has more salt) compared to the human body, it leeches water out of your blood to dissolve the added salt in your cells, and leeches water out through your kidneys while removing the salts from your body. However, it’s nothign to do with toxic salts.
Yes, it’s just too salty. The human body gets rid of excess salt through sweat and urine. But sea water is saltier than both of these. So if you drink sea water, you need more water to remove that salt. Animals that live away from fresh water supplies (sea turtles, seagulls, etc.) can excrete much saltier fluids, so they can survive on sea water.
By the way, I read a long time ago that if you are stranded on a lifeboat with a limited supply of fresh water, the best thing to do is to drink a mixture of two parts fresh water and one part sea water. Not getting any salt is as bad as getting too much salt.