There are no spiritual or moral distinctions among Christians. Because we are all equal, we are all called to submit to each other. Let nothing be done through selfish ambition or conceit, but in lowliness of mind let each esteem others better than himself. We are called to submit in various ways. Likewise you younger people, submit yourselves to your elders.
Submission runs contrary to human behavior.
Earlier, the disciples had argued over who would be first among them. Notice what Jesus says to them in vv.14-17 . In marriage, wives are called to live in submission to their husbands. Women are not inferior human beings who must submit to every man. Being a man, does not make one better than a woman.