How can we esteem others better than ourselves when really we think we are better than others? Some people are better athletes than others. Some are better businessmen than others. Some are better speakers than others, and so forth.
We need to recognize that our accomplishments don't make us better than others. There is a difference between what we do and who we are. Better performance does not make a better person. A person's character can be severely wanting even though his performance is good.
To esteem someone better than ourselves simply means to value them more than we value ourselves. To some that may seem impossible, but it isn't.
That is exactly what Jesus did. If Jesus, who was God in the flesh (1 Timothy 3:16), could humble Himself and value our good above His own, then we should certainly be able to do the same. It can happen when we die to self and live to God.
If we think only about ourselves, we will be selfish. If we get out of self and think more about the benefit of others than the benefit of self, then we will be selfless.