You’re not giving them enough exercise:
If you’re gone 12 hours a day, and your dog’s walk consists of a quick dash into the backyard or your cat's play time consists of tossing some toys at them for just a few minutes then you are not providing your pet with adequate opportunities to use up all their energy. Instead, their excess energy will go into chewing your shoes, stealing your food, or scratching your walls. As the old saying goes, “A tired dog is a good dog.” - which applies to the kitties too!
You haven’t trained them enough:
It sounds like a no-brainer, but if your dog’s training stopped after he learned to sit, lie down, and go to the bathroom outside, you need to up your game. And don’t believe what they say: You CAN teach an old dog new tricks. Try to introduce a new command a week, and practice old ones with him. Besides being able to understand what you want him to do, the mental work involved in him learning commands will tire him out as well. For your kitty friends, a little clicker training can go a long way - you can divert unwelcome behavior, expend excess energy, and get them easily going into carriers to go to the vet or in case of emergencies.
You’re reinforcing their bad behavior:
If your dog is barking for attention, how do you respond? Do you yell at him to stop? Guess what? You just gave him what he wanted. Or if he steals a hot dog roll off the counter, do you yell at him then watch, defeated, as he eats it? Again, you're letting him know his bad behavior paid off. Think about what your dog is trying to accomplish when he’s misbehaving and don’t allow him to be rewarded for it. Instead, give him an opportunity to succeed (for example, tell the begging dog to go to his place and lie down, and give him a treat when he does). Is kitty waking you up in the middle of the night? Playing with them with their favorite wand toy until they are panting which will help them burn their excess energy and you get a full night's sleep!
You don't know your pet's breed:
This goes hand-in-hand with #1. If you have a Border Collie who is terrorizing your home, but you give him a walk each morning and night, you might think you’ve fulfilled the exercise requirement, right? Wrong. While a twice-daily walk might suffice for a breed like a Greyhound or a Labrador Retriever, Border Collies were bred to work and need opportunities to run and “do a job.” A fast-paced game of fetch should do the trick, but sports like agility offer the kind of structure and exercise this breed needs (and you can earn titles and ribbons in the process!). Additionally, if you have a Bengal or Savannah cat you will need to include more enrichment in their lives to keep them happy and healthy.
You’re dealing with an adolescent:
OK—this one isn’t necessarily your fault, but the way you respond to it can make a difference in your animal's behavior. Like humans, animals go through a rebellious “teenager” phase (around 5 months to 18 months). During this time, they’ll often test their owners, seeing what they can get away with. Being firm and consistent with your positive reinforcement training will help establish boundaries. And be patient! They’ll grow out of it.