I don't know Mr. Zeins, but I'm willing to bet he keeps something a bit more intimidating that a can of Raid next to his bed.
Instead of a human being traversing a CTC to kill her ancestor, imagine that a fundamental particle goes back in time to flip a switch on the particle-generating machine that created it. If the particle flips the switch, the machine emits a particle—the particle—back into the CTC; if the switch isn't flipped, the machine emits nothing. In this scenario there is no a priori deterministic certainty to the particle's emission, only a distribution of probabilities. Deutsch's insight was to postulate self-consistency in the quantum realm, to insist that any particle entering one end of a CTC must emerge at the other end with identical properties. Therefore......blah, blah, blah, one-half probability, blah, blah, blah, causative loop, blah, blah, blah, doppelganger, blah, blah, blah, voila! Paradox solved. Or something like that.