Edwin Judge explains that to Greeks and Romans, humility meant degrading yourself.
Humility in Greek and Roman ethics would be a degrading thing. To put yourself down to a level that you were not born to, or that your standing in life did not require you to be in, was disgraceful and debasing. There was no virtue in it at all. You might well be aware of other people, and concerned to do whatever seemed just and reasonable towards them, but there was no sense in which you should downgrade yourself.