Saying that F.E.A.R is the best FPS ever is a bold statement, saying that it's your favourite is understandable but, the best there ever was?
To be fair, it is one of the best FPS games ever and one of Monolith's best games ever, even if I liked Blood a lot more.

Geez, man, couldn't you come with a harder question?
I could tell you my top 5 but telling you which one is the true best? Where do I even go?
Should I say Half-Life that first introduced a overarching narrative on the genre? or Quake 1 that was the first fully 3D FPS that was worth playing? How about Duke Nukem 3D with high level interactivity and levels that actually took place in real-ish locations? Or the obvious with Doom and the full revolution it caused?
It's a subjective thing, the "best FPS ever" is always going to be different from person to person.
If you want my faves, tho:
5. Doom 2
4. Quake 1
3. Half-Life 1 with 2 coming very close
2. A tie between Duke Nukem 3D and Shadow Warrior 97
1. Blood
Honorary mentions:
F.E.A.R 1 (F.E.A.R 2 is ok but F.3.A.R is trash), Return to Castle Wolfenstein, Doom Eternal, Unreal and Unreal Tournament '99, Postal 2.
Those are just the one from the top of my head.