the.com/moral high horse

means To act with an air of superior righteousness, lecturing others from a position of moral superiority you've claimed for yourself.

from From the literal 'high horse' — in medieval and early modern times, people of rank and authority rode tall horses, literally looking down on commoners on foot or on ponies. By the 18th century, 'to ride the high horse' meant acting haughty or self-important, using that physical elevation as a metaphor for pulling rank. 'Moral' got bolted onto the front later, narrowing the swagger specifically to righteousness — so instead of flaunting social status, you're flaunting virtue, real or performed.