The Old Yeller comment was made, and pretty much fits what they had to do:
-Can't keep her around like nothing is changed, you'll be killed by her sooner or later
-Not safe to keep her locked up, it'll turn bad eventually and she'll escape or injure you, or have to flee and can't get her in time, etc.
-Not safe to take her with you, have to guard at all times.
-letting her loose is cruel to her, and risky to anyone else that comes across her. Either dies by zombie, or elements/starvation/injury, or unsuspecting group takes her in and she does this shit again.
Gotta put her down. In this world, not safe to keep her around, and no time/resources/safety to deal with her mental situation to 'cure' her.