You may not be causing it completely, but there are lots of ways to discourage it. Having some attachment makes us feel good, but when the pets get anxious when you are not around thats where some problems arise.
Well, you probably select certain personalities and then encourage and reward the desired behaviors.
My dog and my horse have extremely similar personalities. My Arab I picked specifically because of his personality. My dog was bred by a friend and all her dogs have goofy sweet personalities. I definitely encourage the goofy, happy and a little clingy personality in both of them.