In the room cleaning example, you may have reduced the entropy in your room by ordering it, but you have still increased the overall entropy of the Universe.
While cleaning the room, your body turned (ordered) food into (unordered) heat at a rate faster than if you had not been doing anything.
The garbage can is less ordered.
Anything you do to make one thing more orderly will reduce the local entropy of that thing, but will increase the total entropy of the Universe.
In the case of a black hole, you take something ordered (i.e. whatever fell into the black hole had *some* structure; it was matter made of atoms, or it was light made of photons vibrating at specific frequencies, etc.), and you remove that order from the Universe. eventually, that matter and energy renters the universe as random heat (i.e. Hawking radiation).
So black holes essentially destroy information and order, which is the very definition of increasing entropy.