I was so angry about the cliffhanger in episode 8 that I took the week off, but this works out since now I can talk about the relay while knowing the outcome. Haruka is devastated by his loss to Rin and, being someone who's been swimming all his life for what is mostly the love of the water, is very confused. What Haruka does not know is that his mental distress is just a symptom of his mind becoming genre savvy.
See, in all sports anime, the absolute most important thing is teamwork. People will push themselves beyond boundaries they thought they had for the sake of making their team victorious. In Chihayafuru, this happens in a metaphysical sense, with characters like Sumire finding herself working hard for the team despite originally being apathetic, as well as a physical sense, with Chihaya continuing to playing with an injured hand. In Girls und Panzer, Miho joins the Panzerfahren team for her friends' sake and ends up finding a family in them that helps her grow to love the very sport she started out avoiding.
Sports anime are but a subset of the shows that tell stories of groups of people coming together to do great things, ranging from forming a bad in K-ON! to overthrowing oppressors of the universe in Tengen Toppa Gurren Lagann. These anime show that even though we are all individuals that are unique and live our own lives, we can accomplish even greater things when those different lives come together.
Free! does a wonderful job of illustrating this with the races the Iwatobi team swims at the meet. Despite training intensely, every one of the Iwatobi boys end up losing their respective events, with Rei's loss being the most legit because good lord does it suck to swim a race when your goggles fall off. Even though the boys played to their strengths (which conveniently means a different stroke for each of them), their best was not enough to make it to Regionals individually. By a twist of fate (read: Kou's meddling), the team gets one more shot to qualify.
This time, the boys come together for the medley relay, each one swimming a leg with their specialty stroke. This time, they win. Simply depending on one another supercharges their power and streamlines their performance. This is the X-factor that Rin showed Haru when they swam the relay in elementary school. The solidarity that they feel when competing as a team is why Haru was so sullen after Rin said they would never swim together again and also why Rin gets supremely jealous watching Iwatobi win without him.
The face of NTR
I predict that Samezuka will lose the relay at regionals against Iwatobi and not only because guys on the latter team are the main characters. Rin has grown into an isolated, jaded person; a lone shark, if you will. His attempt to compete against Iwatobi in the relay is misguided and will fail if he goes into it purely to win against Haru. Rin's motivations stand apart from those of his team and will rob them of the X-factor that strengtens Iwatobi.
Finally, I can't end this without mentioning the best part of episode nine: