I am not asking anyone to shoot pets or kick them out. All I am saying is: Dont have them in the first place. Not if you are preparing for possible bad times.
Its like you are going somewhere important ; a busines meeting , a tricky situation, a risky mission ..etc. will you take kids with you ? I will prepfer to be alone or with responsible adults only.
Likewise, how can I predict pet behaviour in messy situations? I can hardly manage crying kids and under-prepared wife ..etc. not to mention my own fears and shortcomings. So, in a survival situation it is better - IMHO at least - to have less dependents and less things to worry about. That means less pets or NONE.
Even in case if I bug-in. With family members suffering from prolonged shortage of nutrition and hygeine after SHTF, pets may become a source (carriers) of diseases, especially if they wander out around corpses of dead animals or sewage or whatever.
Please notice, I am in no way saying : Keep the pet and when you hear that Katrina is approaching take your gun and shoot your pet.
What I am saying is : think about it as a part of preparing for a possibility. If you think the pet could become a source of trouble in SHTF, you still have the time NOW to consider giving it to another loving home. IMHO, you will be better prepared that way. That wheeled garbage can mentioned in the story above could be full of wheat and beans instead of dog food.