As a skeptic and someone that never had a pet, all I see in pets are creatures that are very needy and you have to look after, take care when sick, sometimes with expensive procedures, and are a burden if you have to stay away for any time longer than a few hours.
That said, the furthest to a conclusion I reached for the answer to "why people have pets?" is that pets, mostly dogs, somewhat resemble the reaction that people that love or care about you have with you, although that's arguably instinctive. For example: a Dog seems happy when he see the owner, just like a girlfriend or family member does. And that is usually taken by people as a reason to bound. Other more simple explanation is that pets are cute and we like to have them around.
So is there any scientific explanation to why people have pets?