Major Spoilers...
Barry Allen IS the fastest man (or meta-human) alive. He falsely claims so in the beginning, not knowing there are faster characters in the show later on. He has to train as hard as he can to increase speeds to match enemies and juggle life.
Now, let's talk about Zoom, Savitar and the Kid Flash.
Zoom (Jay Garrick's alter ego) is from Earth-3
Kid Flash is Wally West (just a newbie in the ways of speed). He has lost some races against Barry Allen, whilst Barry teaches him the ways of the "speed force".
Last but not least, Savitar. If you're up to date on the latest episodes, you'll know that an alternate Barry Allen IS Savitar, ergo "the fastest man alive". If you argue that technically this isn't true, then that's another story...