Probably most of us were not brought up this way and yet we can learn to care and share with our non humans by being educated. When children are taught good information which enables them to have an understanding of the issues of non humans they will care. For example, if children are taught about the painful cruelty that may result from the pet trade they will come to the conclusion themselves why it makes sense not to buy an exotic animal.
If knowledge and respect can lead a child to concern for animals then the reverse is also true. Everytime a child sees an animal abused it will become easier for them to do the same behavior.
Children and adults who are kind to and respectful of animals also are much more likely to show respect and kindness to humans as well.
Wishing you kindness and respect for all beings,