It’s fairly simple: if he had not entered the bath, displacing water, the level wouldn’t rise. If you put a chunk of ice into the bath, the level will rise, but if you then measure the new level, then wait for it to melt and measure it again: there won’t be any change. New water has to move from land to sea for the level to rise: you can’t get sea-level rises by melting floating sea-ice.

That is a scientific fact, not up for debate: it is basic (very basic!) physics.

I’m waiting for you to have your Eureka moment…