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This situation is completely degrading to the woman in question. She is living with a man who is hiding her from his parents, won't make a commitment, and refuses to give her the respect and dignity she deserves, while he dances around and stalls.
We can discuss cultural issues all day, but the upshot is that this situation is unacceptable and is not the behavior of a man who truly loves and values his woman.
If I were her I would be either packing a bag or changing the locks on the door as we speak.