Isn't that obvious? He is in no position to look after the kid, and letting her go means she is going to die anyway, and could expose who he was before that.
He is a killer, that is usually his first instinct.
He realized what an awesome responsibility it is to raise a child. He didn't want that responsibility. He never sought it. He resented having it thrust upon him. He also understood how having that responsibility would make him more vulnerable, as well as thoroughly complicate his life.
The easiest way to be rid of such a problem was to eliminate Mathilda, the same way he was used to eliminating other threats to his well being: with lethal force. He's a professional killer; it's how he's used to dealing with anything that threatens to compromise him. Eliminating Mathilda would have been the quickest, most efficient route back to the simple, uncomplicated life he had been living, and with which he was completely comfortable.
But of course, his moral code wouldn't let him cross that line. He could rationally decide this was what was best for him, and step right up to that line, but he couldn't bring himself to cross it.
That makes sense. It was just how he dealt with so many people (putting a gun to their head).
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