Women today largely view respecting men as optional, not as something that the Lord requires of them. The basic idea being that if and when a man earns their respect, then and only then will they give that man respect.
Christianity does not work that way. Men are not required to earn women's respect, any more than Christian men (or women) earn their salvation.
Now, if a man wants to have a relationship with a woman, working or romantic or whatever, then yes, he should try to earn her respect and trust.