"Doesn't it make sense that another Araragi, the flip side of you, exists in this world?"
This is what Araragi experienced during his transition from high school to college. The story of the continuation of the end (Owari).

The morning after high school graduation, Koyomi is standing in front of the mirror above the sink to wash his face when he suddenly feels like his reflection is staring back at him. He instinctively reaches for the mirror, and upon touching it, his fingers sink in...

When he comes to, Koyomi finds himself in a world where everything appears to be reversed.

[Source: official English website]