How does Vincent save his brother if he never saved anything for the swim back?

Summary: One of the central themes of the film is that people can overcome their physical limitations through strength of will. Vincent's will exceeded Anton's, so he persevered when both of them were at their physical limits.

Anton's willpower was atrophied: Anton had spent his life to that point being told exactly what his physical and mental limits were, and abiding by them. Every time he swam against Vincent, he won because of his innate physical advantages, not because he tried harder. He never had to try. He didn't know how to try. As soon as he felt like he was at his physical limit, he panicked and began drowning. This is akin to a soldier's first day in boot camp, having to push their body to its limits for the first time: everything in his head was screaming "something's wrong".

Vincent had an iron will: Unlike Anton, Vincent was constantly told what that he was naturally inferior. His life was a constant struggle to prove his worth. Every time he swam against Anton, he gave it everything. He knew that he could keep going, even when every part of him seemed to be failing. This is mirrored in the scene on the treadmill, when he has to pretend to have an easy time, even though his heart is pounding through his chest. He is like a veteran soldier, well-versed in ignoring the instinctual limits his mind has placed on his body.

I disagree with a couple of details in Liesmith's otherwise excellent answer. The core point I disagree with is that people can:

... overcome their physical limitations through strength of will.

People can't overcome their limitations. They can only overcome their perceived limitations. This is the key to the movie. People are being told left, right, and center that they can't do XYZ because of their perceived genetic limitations. Vincent achieves success because he drives himself to excel despite the limitations everyone tries to impose on him.

While Vincent is running on the treadmill Anton asks Director Josef if it is possible to exceed your potential, to which Director Josef responds:

No one exceeds their potential. If they did, it would mean we did not accurately gauge their potential in the first place.

This is a very true statement. This society wasn't gauging people's potentially accurately, because spirit/will can be the deciding factor despite a clear genetic/hereditary advantage. This is acknowledged obliquely by Jerome when he states he came in second in the swimming competition even though:

Jerome Morrow was never meant to be one step down on the podium.

So how does any of this relate to your question?

At the meta level, the swimming competition was about overcoming society's expectations, and the fear of not being able to accomplish your goal in the face of the odds. Vincent can only succeed at Gattaca if he overcame his fear of failure, and ignored society's expectations.

At the stated level the swimming competition was a game of chicken. Chicken is all about fear management, and confidence in your ability to handle the outcome regardless of what happens¹.

If you watch again there are three key swimming scenes.

1. Everything goes as society assumes, and Vincent fails.
2. Vincent out swims Anton proving to himself that he can defy society's expectations.
3. This is the scene you're talking about.

During the lead up to the third swim Vincent is actively taunting Anton, and this continues while they're swimming. Anton continually expresses fear, uncertainty, and doubt during every bit of dialog while they're swimming. He starts the dialog by saying.

Vincent where's the shore? We're too far out.

Vincent responds by taunting Anton, so they swim on. Next Anton asks Vincent "how can you do any of this?" and "We have to go back." Vincent replies:

We're closer to the other side

He is really saying: "Are you feeling tired because I can go forever" even though this isn't true. The taunt isn't about the truth. It is about breaking Anton's will². Incredulous Anton asks:

What other side! Do you want to drown us both?

Then Vincent gives the line you mentioned:

You want to know how I did it? This is how I did it. Anton, I never saved anything for the swim back.

This is both a taunt and the truth. The taunt is confirming the implied willingness to drown them both that Anton voiced. The truth is Vincent eschews the fear of failure, and is willing to sacrifice everything to prove society wrong.

And finally, he did in fact have the strength to save his brother otherwise they both would have drowned. Anton needed to be rescued because:

• Anton wasn't in as good of shape as Vincent, and Anton was actually the one who didn't save anything for the trip back.

OR

• Anton gave up mentally so he couldn't access/use his remaining strength³.

Either way like it was mentioned in Liesmith's answer and in the comments below his answer, Vincent wasn't saying "I don't have the strength to swim back."

¹: ^{Note: these are the same skills that Vincent needed to succeed as a "borrowed ladder."}

²: ^{Before they get hypothermic and/or both don't have the strength to swim back.}

³: ^{This is what happened IMO when they were boys and Vincent got tangled in the seaweed. For symmetry reasons I like this as the reason why Vincent needed to save Anton both times.}

From a spiritual perspective, it's a "one-liner." You always have what you need, and always when you need it. When you live in the moment, and care only for the moment, then nothing else matters and your all is all you will ever give. You will always exceed when you don't consider the what-ifs and try to prep for the future. The whole moral of the movie is: You are everything and more. The whole DNA scripts predicting people's future were proved irrelevant. Your future does not matter, and when trying to live for the future you will never be your best, because you're only your best when you are in the moment. Living in the now and giving your all is the motive and moral story of life. You always have what you need for the task at hand, and expectations should never exist, who are you trying to please? Who do you have to satisfy, other than your internal desires, and then-who/what has shaped those desires? If you really ponder the questions, you'll realize that you only want to be yourself, which comes naturally. You are taught to compare yourself to others, your ego is competitive, but you really just want to BE and do as you please.

I just watched this movie last night by the way, and the ending made me cry. I typed this just to drop my 'two cents', no academic, edited, well-thought out response lol....just straight from the heart!

Just to say, I'm a long-distance open-water swimmer - did a 24 mile swim of Lake Washington, and an 11 mile swim from US to Canada's Vancouver Island, a 5 mile swim from British to US Virgin Islands.

This Gattacca quote has always been the way I train and stretch my limits. I just swim out until my energy flags and I can't face anymore. At this point I could paddle back to shore, get out, get my cellphone in my drybag, call for pickup, walk barefoot through private property to get to a pickup location, figure out how to collect the gear at my departure point, tell my buddies that I couldn't make it.

But actually it turns out easier and more convenient just to swim back. Willpower, stubborness, irritation, pride - they've always been able to take me twice as far beyond what I thought my body could do.

(I'm never far from shore or rescue boat, and always have a personal safety swimming buoy. I use irritation and pride as my motivator, not fear of death!)