Gryffindor cared about courage, yes, but not purely physical courage. There's also the emotional courage to speak up when something isn't right even when people you respect don't agree, and the intellectual courage to face the truth no matter what it is. He saw the study of magic as fundamentally practical, oriented towards achieving things in the physical world alone or with a group of allies.
Ravenclaw saw magic as primarily an intellectual pursuit, a quest to understand the true underlying laws of reality. She loved curiosity, the urge to know for the sake of knowing, to share that knowledge with all who sought it, and to use it for the benefit of all.
Hufflepuff was the glue that held the other three together. She cared about friendship and loyalty and hard work, but mostly she cared about people. She saw wizardkind as a community, and the study of magic as a way to strengthen that community and preserve that culture. She cared more than any of the others about making sure every magical child she could reach had a home at Hogwarts.
Slytherin has a reputation, these days, for caring about the magical pedigree of his students more than anything else. And he did care about that, but not exclusively. He saw magic as a gift and a responsibility, something that not everyone was ready to use. He cared about the magical community and wanted to protect it from threats both internal and external. But he also cared about cultivating his students' talents. He believed in intelligence turned to practical ends, in the usefulness of knowing friend from foe and understanding what people want and how to work together with those you disagree with for a common end. He believed in finding the people with the will and the ability to do great things, then nurturing their talents and encouraging them to reach ever higher. His flaws have shaped his legacy more than any of the others, but his virtues were real virtues and many of his students accomplished great good in the world.