The reality is that for many people, publicly expressing ideology is not about trying to say what's right and wrong; it's about trying to look good to others. It's moral masturbation, not moral theory. Rather than helping others — which might cost them something! — they advocate helping others. Rather than ameliorating some of the bad effects of injustice — which might cost them something! — they advocate for justice. They then consume the warm glow of cheap altruism and earn the admiration of like-minded peers, all while living a self-centered luxury lifestyle.
The George Mason University economist Tyler Cowen once noted that in the United States, cities' politics and behavior seem to be at odds. Egalitarian cities with fairly equal distributions of income tend to have a conservative ethos, while cities that have massive disparities in wealth and that shower rewards upon high-status people — such as Los Angeles and New York — tend to have left-wing and egalitarian ideologies. One possibility is that wearing a left-wing ideology is a sort of cover for living a right-wing life. Perhaps this partly explains why elite universities are so left-wing. They sell elite status, but they cover this up with incessant praise of social justice. It could be that Harvard is a right-wing institution that undermines social justice, but if it never stops talking about equality, maybe you won't notice.