A SINGLE WOMAN I know wanted a child. She had to decide between adopting one or using some man to do what neither she nor anyone else has ever been able to do alone. She opted for adoption, saying that there were already too many babies in the world but recognizing also that thank God, there is a difference between a man and a rooster.

I cite the case of this woman because it points up in an almost absurdist way just how irrelevant Daddies can be. Here is a lady who wanted a child but no husband and who, given her income and her education, was perfectly capable of going the entire motherhood route on her own. In fact, when last heard from, both mother and son were doing fine. As for a husband, none was even on the horizon.

There is little doubt that the "pro-family" people who lately have been waxing eloquent over that great cliche -- "the traditional American family" -- and who have turned to politics to ensure its preservation, would not consider the lady nor her son for membership in their movement. The reason for thast is that these people are not so much pro-family as they are pro-Daddy. Like other failing institutions, he needs government help.

And he may be getting it. You could go through the Family Protection Act authorized by Ronald Reagan's ally, Sen. Paul Laxalt, and just keep inserting the word "Daddy." It appears either by implication or by suggestion over and over again, and many of the issures that the proposed law addresses are those where Daddy, the traditional one, at least, seems to be losing his authority. He cannot spank, say no to abortion, reject sex education or deny contraception to his children. What's Daddy to do?

The truth is, of course, that Daddy -- the sterotype of a father as played by someone like Robert Young on the television show, "Father Knows Best" -- is in trouble. Increasingly, he is less and less crucial to the economical survival, not to mention well-being, of the family. Women work and when they do the law insists they get the same pay as men for the same work. It might be silly to say that a man's economic worth to his family is diminished by his wife's labors, but it's safe to say that it is certainly not enhanced.

What is left after the bringing-home-the-bacon routine has turned into a farce is simple -- not much. There is Daddy as Ultimate Authority, but even here both the state and common sense have intervened. Daddy can no longer beat either his wife or his child without answering for his actions. He can not tell his children about the birds and the bees when he wants to because the schools will do it when they want to and he cannot even stop a child from procuring contraceptive knowledge or devices. Even when it comes to a wife or child having an abortion, Daddies need not be consulted.

The total picture for the traditional Daddy is not a bright one. His authority has been eroded, his status diminished and even his once-unquestioned privileges in certain sexual matters (the old double-standard, for one), is under strong and unrelenting attack. His oldest role, protector of the family, is gone. Indians no longer raid at night and women are as good as men at calling 911-- and then getting the hell out of the house.

The upshot is that some men -- and some women, too -- yearn for the supposed good old days when Daddy, bless him, was Daddy. That their remembrance of things past probably does not conform to reality and that there is, in any case, no going back, seems almost besides the point. What is not beside the point is that just when liberals are giving up on the belief that government can do very much at all, conservatives think it can affect, of all things, the family. There is something poignant about it all. It would be nice if one group could learn from the other.

But they won't, or they don't. Instead, you have this yearning for the American Family of Old, for the Daddy of myth -- a myth believed mostly by the Daddies themseleves. It fuels an entire political movement.

To Daddies who see their world crumbling around them, who see no dogs bring slippers, the way things are going may seem threatening enough to justify a law or two to prop up old order.

But there are a whole lot of others who have no yearning for the old days who are grateful to be free from the need to be the provider, protector and family policeman and would not welcome some mandated return to the fatherhood of yesteryear.

They would prefer to be something other than the traditional American father -- like a true marital partner and a better Daddy.