Whenenever I try to verify the game cache of Skyrim I always get the following error: 1 files failed to validate and will be reacquired.

I have already tried the following solutions:
1. Reinstall the game.
2. Refresh Steam (deleting everything except Steam.exe and the steamapps folder).
3. Reformat PC and download everything again.

What is causing this error?

Giant overreaction to what's not even a problem. All it's doing is redownloading one of the .vdf files for Steam that has nothing to do with the game.

The better question is why are you trying to revalidate the game so often?