A violin with no strings

Romani people have an interesting proverb: “A tent without a woman is like a violin with no strings.” This gives an idea about family life and emotional needs. There is no song, rhythm, music, melody, or harmony. Man felt alone in the Garden of Eden. The Lord gave him a woman, Eve, as his wife. (Genesis 2:18)
Good creation: God’s plan is complete and perfect. God found the creation of Adam to be good. So, Adam was spiritually, mentally, emotionally, psychologically, and physically fit and good. He was neither incomplete nor imperfect.
Loneliness: However, God intended and designed man to be a social being, living in a community, and in relationship with other humans. So, Adam felt lonely as he did not meet anyone like him to talk to, have a conversation, and eat together. Though he could speak only to God, but not speak with other humans, as they did not exist. Perhaps he watched animals communicating with one another with sounds, gestures, and noises. He needed a counterpart that would be of a similar nature and capacity.
Purpose of God: God’s purpose was that humanity should be fruitful and multiply and fill the earth. For that, Adam needed a partner, suitable to help and compatible.
Creation of Eve: God put Adam to deep sleep. Then he took a rib of Adam, closed his flesh, and created Eve. Matthew Henry wrote: “Eve was not made out of Adam’s head to top him, not out of his feet to be trampled upon by him, but out of his side to be equal with him, under his arm to be protected, and near his heart to be beloved.” Eve becomes the strings in the violin.
Meaning: The creation of Eve teaches three important aspects regarding women. First, equality: women are not inferior to men. Second, a husband and wife are partners and collaborators, and not competitors. Third, a perfect companion, having dignity, to be loved deeply, and nurtured carefully. Hence, Adam should keep her close to his heart and provide protection.
Do I understand God’s intention in the creation of women?