Barry wanted to get faster so he thought that the only way it can happen is for him to learn from one of the two people who are faster than him. The first one is Zoom, which is not possible because the villain is on Earth-2 and facing off with him means risking his life as well. The second one is Eobard Thawne or the Reverse-Flash himself.
He knew he could pull it off with Eobard Thawne since the man was disguised as Harrison Wells and he also deals with him a lot before the big reveal during the Season 1 finale.
Just like the time travel he did during the early part of Season 2, Barry travelled again in time without tipping off his STAR Labs team.
Critics believe that having the Season 2 Barry going back to Season 1 was quite excellent and executed brilliantly. It was a delight for fans to see Eddie Thawne once again and Barry acting as a concerned brother to Iris.
It was also a joy to see Barry fighting himself immediately after he travels back and it was only Cisco Ramon of the past realized what was going on. It was also quite satisfying to see the present-day Barry interacting with the past Harrison Wells, looking into the eyes of the enemy before his enemy betrayed him.
Episode 17 of “The Flash” was one of those sweet spots episodes of the show, playing with time for big dramatic and emotional effect.