why does a man go down on his knee when he's proposing?

Knights bend down on one before the king when being knighted and when presenting themselves in a show of honor to royalty. In war, the losing party would kneel in front of the army who won the battle in surrender.

Respect. Honor. Surrender. Those are the reasons behind the bended knee in a marriage. As a sign of respect, the man lowers himself as an act of humility before the woman he desires to spend the rest of his life with.

Furthermore, when he is on one knee, the man is faced to face with the woman’s womb, where life is created. He is honoring her body and honoring her as the Lord’s creation, which deserves to be revered.

A man is surrendering himself and the rest of his life to her. He is surrendering bachelorhood for fatherhood in promising to raise children with her and remain faithful to her in all things.

Source: google