There's no such thing as 'breeds' within scientific classification. I don't even think you're using the term 'family' correctly.
If God created all animal "families" why can we trace the evolutionary history to species that existed previous? If 'cross-breeding' is actually how it happened, then we should be able to see and trace what was cross-bred when. But as it turns out, that's not what we see in the natural world. There are some, ligers, donkeys, but they are few. If cross-breeding was how we got the diversity, we should be able to trace what species they came from. Hell, if cross-breeding was actually true, all the various species should have the same age, except those that are cross-breeds. That would be the point where, as you say, 'God' created it all. But there isn't, various species have various 'ages' so to speak. They don't have a uniform one. Going further, if it was all created, then why do we see some species arriving on the scene at various points in time, and then going extinct. Why do we see most modern animals arriving relatively late to the party after the billions of years of life's existence on the planet? What were they cross-bred from? Life after all, tends to gear towards organisms of larger complexity as time marches on. Cross-breeding would not explain this.
You begin to see just where this 'cross-breeding' thing ends up not explaining a lot of what we see in modern biology.
And as it turns out, there's no evidence to suggest things were simply created as they were, remained unchanged for all time, and then more organisms created via breeding two species. If that were the case, we should be able to see that sort of trend in the various forms of evidence. But instead they indicate towards the modern theory of evolution.