Honour comes from God and our connection to Jesus. We honour Mary in connection with the child conceived in her womb.
Mary came to Elizabeth, and following the culture of her time and place, Elizabeth had the higher honour. Elizabeth was older and married, so she waited while Mary came to her.
Through Jesus, God reversed things, suddenly and dramatically.
Respect and honour are very different in our culture. We often shy from expecting recognition and pride ourselves in being treated just like everyone else. However, people are still treated with different levels of respect.
Whom do you honour in your life? Who are the people you respect? When do you expect recognition?