The Barn Zombie Slaughter:

Hershel's outrage aside, there were two good reasons to shoot the zombies: 1) put them out of their misery (are zombies miserable?), and; 2) that rickety old barn was not secure like Fort Knox or even Mayberry's jail cells.

Hershel was oddly passive during the shooting. Going to be interesting to see what he does in the next episode on February 12.