>

In the US, 25 states already regulate breeding and require a license... with more added every year. 
So, your view is sort of what's happening.
You mean that you can't own two dogs of different genders if they are both capable of breeding? >

Sorry I didn't clarify. Dogs should be able to have litters of puppies and allowed for them to be given away, but it should be regulated with a license to practice when considered as a business. >

What makes it a business? >

Whatever you have to tell the IRS. >

Many people run a "business" and never claim anything to the IRS. And those that do probably have a license to operate as a breeder by their own municipality >

Whether people do it or not, its illegal. >

But that's the issue. If they sold one puppy, that would be a business, right? So if anyone has a puppies, you are fine with them giving them away, just not exchanging money for them? >

There is a difference between breeding golden retrievers that sell for thousands a pop, and providing a homing fee to someone trying to buy an animal. If the small-time breeder isn't doing enough to alert the IRS; then they probably just aren't a big enough fish to fry.