In White Rabbit he said, "I don't swim." Very different than I CAN'T swim. He may have been able to swim a bit but not enough to save someone from drowning. He also may have been using his heroin recently and may not have trusted himself with someone else's life.
As for the claim to be a swimming champ, he knew he just needed to sink to the bottom and wanted to go do that since he believed Desmond when he said he had to die to save Claire. He wanted to sacrifice himself and didn't want to get into (YET ANOTHER) argument with Jack.