I was turned down for a dog after I had to return one that was aggressive with my grandchildren. She only liked me. My vet advised me after examining her and assessing her aggression which should have been done before I fostered her.
My daughter decided she could not bring the grandkids to my house because they had a dog they climbed all over and didn't understand they had to stay away from the one I had. The dog bared her teeth when they walked in and went for them. I am all for rescuing. I've had four rescue dogs, my cat and a few guinea pigs. Because the rescue decided I was "fickle" they kept turning me down so I moved on to a dog advertised in the newspaper. A wonderful dog.
I've also been turned down because I didn't have a fenced yard. I had 7 acres! It may be easier to adopt a child than a dog these days!! You don't need a fence to adopt a child.