I deleted my first comment on this because after checking the source, I found that I had spoken hastily.
The idea of "esteem others better than" self is not talking about whether they are or are not a better person but rather whether I am able to "get over myself" to such a degree that I am not in any way engaging in self-aggrandizement but rather in giving respect to others. Regardless of whether a person deserves or does not deserve respect, I need to place the giving of respect to others above my desire for others to respect me.
Humility is not so much about being scum as it is about being admirable and yet not seeking to be praised. I heard a story about a man who was commenting to another about a third man. Of the third man, the speaker said "He is a great man but he does not know it."
I don't know whether the speaker intended that to be literal or to mean that he does not let it go to his head or affect him, but the point is that true humility always places others and the need of other ahead of ego.
It is a very small man indeed who needs to be seen as great. It is a great man who can be the wind beneath the wings of everyone else so that they can soar.