"It is statistically proven that the strongest institution that guarantees procreation and continuity of the generations is marriage between one man and one woman. We don't want genocide. We don't want to destroy the sacred institution of marriage"

This quote by Alveda King is emphasizing the significance of marriage in between one man and one lady. She is suggesting that this type of marriage is the strongest organization that guarantees procreation and connection of the generations. This is likely a referral to the fact that statistically, heterosexual marriages are most likely to produce kids and hence guarantee the extension of the generations. King is also indicating that any other type of marital relationship, such as same-sex marital relationship, might result in the damage of the sacred organization of marital relationship and even genocide. This suggests that she believes that same-sex marriage is a danger to the conventional institution of marriage and could lead to the damage of the generations. Ultimately, this quote is highlighting the significance of conventional marriage and the need to protect it in order to ensure the extension of the generations.