#fighter battlemaster

Firstly, and most powerfully, this feature can be used as a way of identifying monsters disguised as humanoids;

If your Strength Score is 16 "Know Your Enemy" can be used to detect Hags*, most Lycanthropes but not wererats or werewolves, Oni, and Vampires and Vampire Spawn* as their Strength Scores will be greater than yours except for Green and Sea Hags and Vampire Spawn who will be equal to you. Note Knights and Berserkers will be equal to you and Gladiators will be greater than you without being monsters.

If your Dexterity Score is 14 "Know Your Enemy" can be used to detect Quasits, Imps, Dopplegangers, Jackalweres, Liches, Rakshasa, Succubi/Incubi, Vampires and Vampire Spawn, Assasins, Bandit Captains, and Spies as their Dexterity Scores will be greater than yours. Note mages will be equal to you.

If your Constitution Score is 14 "Know Your Enemy" can be used to detect Yochlols, Dopplegangers*, Liches, Werebears, Wereboars, Weretigers, Werewolves*, Oni, Rakshasa, Vampires and Vampire Spawn, Assassins*, and Bandit Captains*. No asterisk means they're greater than you, asterisk means they're equal. Note Knights will be equal to you and Berserkers and Gladiators will be greater than you.

If the subject in question is known to be able to cast spells of a level equal to greater than a caster of your level, but they appear to have fewer class levels according to "Know Your Enemy" then that's a monster! Note does not work with liches as they are 18th level spell casters.

You may also be able to use AC to determine if a subject has natural armour, but that's a more complicated process and may involve talking to them in various states of dress yourself.

You may also be able to use HP to determine if a subject is unusually powerful, but again this is a more complicated process and may involving intentionally getting yourself beat up in sparring matches.

Anwyays, this knowledge can be incredibly useful for determing if the person serving you tea is actually a peasant, or someone sent to kill you, or if the local count is actually an undead monstrosity, or if your best friend has been replaced by a doppleganger, or if the centipede hanging out in the corner is actually a demon. There is no Nystul's Magic Aura to hide creature types from divination, no Alter Self or Illusion that will bypass this. The only thing that can bypass it is polymorph but that comes with a bunch of stat drawbacks.

Now, there are a couple problems with this.

Homebrew. The numbers I used came straight from the original 5e Monster Manual, but homebrew may budge the numbers enough to make this unreliable, however it is still a good tool for narrowing things down.

This may be considered to be metagaming, which I'll argue it is only in some cases. If you note a stat and then turn to your party and say "okay it is one of these things" and show them one of these lists, probably metagaming. If you notice the frail old woman selling apples could arm wrestle a Knight and that makes you suspect that she may not be a frail old woman, probably not metagaming. As always talk with your DM and your Party before you make a character that will push the boundry.

"Know Your Enemy" also has other advantages. If you are in a position to observe someone you're about to fight, such as you're in stealth scouting, then this can tell your casters what to target in terms of Saving Throws and if attack roll spells are a good choice. It can help you identify leaders to be taken out first, just generally a good tactical tool.