Diseases that can cross between animals and humans are called zoonotic diseases and they aren’t super common. The old colloquialism that dog mouths are cleaner than human mouths stems from this, the truth is more that the nasty things in a dogs mouth don’t affect us (much).

Because they can’t catch most human diseases.

To get the maximum benefit per vaccination, it’s best to vaccinate the individuals at greatest risk of spreading the disease first. And in most cases, diseases that affect both humans and domestic animals spread far more quickly among humans, thanks to their larger and more heterogeneous social networks. So even if your aim is just to protect the dogs in a given community, you’re probably better off vaccinating x number of humans in the community than the same number of dogs.

Not all diseases have the potential to mutate in a way that will affect dog or vice versa

Because they don’t.

Maybe they can be carrier but don’t get sick.

Flu or cold for example…