OK so here is why the ending of Soul Eater ( anime ) makes since.
So if you were listening to Maka's little speech she said how it was her turn to be brave. Well, this anime was trying to say that bravery can defeat fear.
And earlier when Maka and Soul used the witch hunter attack Asura said that he was no demon all he was, was fear.
So when Maka let go of her fear the power that Asura held over her was no more. Asura was know weak and Maka took this time too attack.
She collected all her bravery into her fist and falcon punched Asura. Therefore transferring a small part of her bravery into Asura. By doing so Asura was no longer just fear and was " killed ".
"So bravery is just like madness, it's in everyone" this was the final thing Asura said. This is important because this helps explains his death. Know that Maka was able to find the weakness to the Kishen everyone would start to do this. And it would be easier for them because they know it lies within them. So Asura, finally seeing this, surrendered or was killed because he was no longer fear, nor human, nor demon, he was nothing.
