The movie leaves it a little vague, but his brother disappearing would wrap up the plot nicely, as would his brother finally seeing the Vincent's perspective and keeping his mouth shut. On a broader level it's the "burn the ships" strategy; nothing motivates like having no alternative.

He didn’t limit himself planning for the future, rather he found that when the time came he had strength he didn’t realize he had.

Also, he quite likely _does_ die in space. Which figuratively but very directly represents not leaving anything for the swim back. There is room to square the main message of the movie about transcending limits with Gore Vidal's line (something like) "No one exceeds his potential... It would simply mean we had failed to accurately assess it in the first place." Maybe he makes it back, maybe he doesn't, but he goes, does what he sets out to do with no consideration of whether he will be able to return and then tries to return. It's exactly equivalent to people who say they would go to Mars even without knowing whether it is a one-way trip at the outset.

The one I didn't really understand was "It's too late for that. We're closer to the other side."

He is willing to die to succeed. If that meant in that moment to outswim his brother he had to drown then he was willing to do it. His brother was limited by his fear of death and his subconscious need to still turn around and swim back. He had no concern so was willing to go as long as it took. It just so happened that he was physically fit enough to be able to make the return swim as his brother quit in time.

That's the whole point though, right?

Anton's top priority was to not drown. Vincent's top priority was to win (Even if it resulted in his death).