Good question. There are several reasons to armor and strengthen your pet.
In East New Barkston you have the Armory. Here you can add armor to your pet.
But before you can armor, you need to have armor in your backpack. You can find armor at Padam's Shack. The pile at the backyard is the armor pile.
How long it takes for armor to be added, depends on the amount of armor your pet is already carrying:
Click here to find out how to strengthen your pet.