The Flash is said to be the fastest man alive, but from season 1 there have been people like Zoom or Savitar, who are faster. So is Flash really the fastest? And if so, how?
Typically any foes who are faster than the Flash end up with a nasty case of "Deceased, temporally displaced, or otherwise no longer currently alive."
When Flash says he's the fastest man alive, you should take it as a warning to not try to go faster.
In all seriousness, though, he does generally tend to be the fastest man alive. His enemies who are faster weren't known when he first made that claim (For instance, Reverse Flash wasn't known to exist - by Barry - for many episodes early in Season 1) or aren't considered 'men'. Savitar, for example, is known to be a God of Speed, and not suspected to be a man.
And, of course, Barry's boast is proven definitively true when we discover who Savitar really is.
Once it got established as his catch-phrase, there really was no use in changing it just because someone from another universe or hopped up on drugs or from an alternative future or who never existed but temporarily does just happens to be (for a brief moment) slightly quicker.
From the story-telling point of view, many stories follow the same pattern:
- An initial status-quo
- Some dramatic event changes the status quo and put the main character(s) in a dangerous situation.
Many problems occur where the main character and his/her allies prove their value. In Flash, this usually take a classic Monster of the Week form.
After solving many problems, the hero wins and return to a new status quo, usually different from the initial one.
Most stories take liberties from that scheme, but The Flash follows it quite well. The "I am the fastest man alive" voice-over is an introduction to the series and its initial status quo. It is not meant to be an actual description of Barry Allen at the time of the episode.
IMO, the season 2 follows the classic structure the closest: at the beginning of episode 1, Barry is the fastest man alive (true because our knowledge is limited to Earth-1) and Central City is safer than ever, then Zoom comes on Earth-1 and challenges this status quo. Many monsters of the week ensue, until Zoom is ultimately defeated. New status quo: Barry is now the fastest man alive in three Earths at least, Central City is safe... of course, this does not last long because of FlashPoint.