Hmm.
I wonder if this demon tried to defend herself because a human attacked her (a novice exorcist who want some easy fame for exemple), ot if she attacked him because of a sudden urge/Instinct...
Genuinely felt sad when he hugged her for the last time. I had a flashback to the time I hugged my dog the morning he died. I'm not comparing or anything, just saying, don't forget to give hugs to your pets or loved ones.
It hurts even more when you realize that this demon girl was mature enough to recognize the gravity of the situation.
When Evan showed up she knew what had to be done.
She chose to die so that the one person in the world who showed her any kindness wouldn't get into any trouble, and now Evan is forever wracked with that guilt.
Regardless of whether it was self-defense he didn't "have to" kill her. He chose to kill her, because the author needed to cast him as a tragic character.
Not to mention, if he won't do it, another exorcist will. A human was killed, so there's no way he can sweep it under the rug or pretend he didn't see anything.
If anything this was probably a mercy for the girl, since the exorcists probably won't stop hunting her with blood on her hands.
So there was a previous demon girl that was in love with him and eventually her demon nature took over and he had to exorcise her? He blames himself because he treated her like a burden and did make time for her.