On this point, pets are a lot closer to chatbots than to humans. You buy them, you have ownership of them, and they've literally been bred so that their genetics makes it easy for them to grow attached to you and see you as a leader (while their brethren who haven't had their genes changed by humans don't do this). It's normal for people to use their complete control over every aspect of their life to train them in this way as well.
Your pet literally doesn't have the ability to leave you on its own. Ever.