Why would they want a "normal" family when they despise "normal families"?
The left's agenda for years has been the complete destruction of the traditional family. They pushed through the "sexual revolution" to negate the need for marriage and there is still no emphasis on heterosexual marriage. They want homosexual marriage because it will "cheapen" the meaning of marriage for the rest of us. Same with children, the push is for heterosexuals to enjoy sex, but not have children.
Who says they "despise" normal families? Did they come from normal families or from homosexual families?
How on earth do you know what they despise or what they admire?
I lived in the San Francisco Bay Area for over nine years before leaving California. Two of my landlords were gay, and I shared a house with one of them for a year. The small town where I have lived for the past twelve years has been called a "gay Mecca." There is a lot to dislike about homosexuality, but I can't recall ever hearing a gay person say that he or she despised normal families.