The Meaning Of the Net
Throughout the series, a net has been an occurring prop throughout the show that's important is keep secret right up until the finale:
Throughout the show, Takumi struggles with self-acceptance and also a general and frequently declared hatred of Orphnochs as a species. After the Kusaka and Kiba fight, Takumi who had been straddling a line of trying to be the "better Orphnoch" who likes humans suddenly declares that he's returned to his full on hatred of them and even he should die, resulting in him going on yet another self-destructive path.
When he finally comes face to face with Kiba who has completely rejected all previous love of humans and no longer believes Orphnochs are human, Takumi realizes he still can't kill his friend. He's talked big about hating Orphnochs but at his core he still does believe that they are human. So he spares Kiba's life.
Then we see the net again at that moment of truth. Things are blurry first but after we finally see him clearly through the tear as he declares that his final resolution is that Kiba is human and by extension all Orphnochs are. After this Takumi walks through this net that has been placed by man-made means because he's realized the lies that they've been fed about Orphnochs and Humans being so different is something that's simply a false construct and lie. He's accepted himself fully and he can leave.
At that same moment, Kiba is still rejecting Takumi's statement and is unable to pass through. The net could easily be stepped around if he were to become aware of his surroundings but he's still stuck in the belief he's been fed about Orphnochs and Humans being unable to co-exist. However, after spending more time thinking about Takumi's words, he is eventually able to come to a shaky conclusion and realization where he isn't quite sure if there is a correct answer but he knows he wants to support Takumi. So he slowly begins to leave and move past the net.
And by the finale we see the net show up one last time, but completely ripped open to show Takumi with his friends. This is right after Takumi has accepted his fate but also has finally found his dream; to protect other people's happiness, no matter what.
So in the end the net is about self acceptance and looking beyond the blinders that society tries to put on you.