The relationships between animals and people are much simpler and less conditional than those between people. When an animal demonstrates an emotion, whether it's anger, frustration or love, the emotion is genuine. Also, animals do not have expectations as people do.
If people could relate to one another as easily as animals relate to people, instances of conflict in society might be much fewer. One reason for this is that animals don't have needs that are as numerous or complex as those of people. As long as a dog's owner keeps his bowl full of water and food, pets him now and then, takes him for walks and plays with him, the dog is happy. People have many more needs, which is why coming home after a stressful day to a dog is much less risky than coming home to a significant other who may have had an awful day herself.
It helps that dogs do not have the same sort of memory as their human counterparts. Dogs tend to categorize memories by the area in which they happened, the rules they are expected to follow or their own instincts. They can remember that using the bathroom outside gets them a reward, while using it on the new carpet brings discipline, but they don't make the emotional associations that people do to events such as those.