IT HAD TO HAPPEN sooner or later. First men got custody of their children. Then women began paying child support. And now this week a Maryland woman was jailed for failing to pay child support to her former husband, and the judges involved made it sound like they had struck a resounding blow for the Equal Rights Amendment.

"The ERA means rights," declared Prince George's Circuit Court Judge Vincent Femia when he released the woman after eight hours in jail. "But it also means responsibility," he said, neatly overlooking the fact that the Equal Rights Amendment has not been ratified.

The facts of the case are, briefly, that Linda Jean Miller, a bartender who earns $6,000 a year, was divorced last May from her husband William, a carpenter who earns $20,000 a year. William received custody of their two children. Linda agreed to pay $30 a week in child support and was supposed to have reasonable visitation rights.

She says the couple agreed he would care for the chidren because he was living with his parents and "would have a babysitter there all the time." But, she says her ex-husband subsequently refused to let her see the children, aged 6 and 8, except at his parents home. She says he wouldn't let them stay at her house on weekends because she is living with her boyfriend.

She says when her ex-husband curtailed visitation rights, she refused to pay child support. She says her employer and a lot of friends helped her pay the $2,000 she owed her ex-husband so she could get out of jail. Now she is going to court and "get the visitation rights straightened out."

William Miller says his ex-wife has not visited the children since August and he has pursued the child support "to get her attention. To let her know she has two kids." He tells of Christmas presents that the children put under thetree for their mother that she never came by to get. "The whole thing makes me so goddamn mad I don't know what to do about it," says Miller. "The only thing it's doing is hurting my kids."

The voices in this divorce are different in that the man is saying things that women have been saying and the woman is saying things that men have been saying. But if you listen to the voices, you hear the same bitterness, the same accusations and you realize there is the same tug-of-war going on between payments and visitation rights that is typical of divorce.

Barbara Bergmann, a professor of economics at the University of Maryland and a member of President Carter's Price Advisory Committee, is working on a book about the American child support system, which she says simply doesn't work. She would overhaul the entire child support system and federalize it. "The reason it has to be federalized is so that the absent parent can't flit from state to state. We also need a system which takes charge of the collection and where a person is supposed to pay and knows if he or she is delinquent, there are going to be some rather speedy retributions and it won't just be forgotten," she says.

"In a lot of these cases the payments and delinquencies are tied up with disputes over visitaton rights. I think if the payments were handled in a more businesslike manner through payroll decuctions, like social security, that would disentangle that issue from visitation rights." She believes a more businesslike approach toward deducting child support payments would improve the chances of children maintaining regular contact with both parents.

The child support system is not just something personal between the Joneses up the street or the Millers in Maryland. It's something that has to do with everyone paying taxes. The Census Bureau has developed figures, based on a 1975 population survey, that indicate that only about a quarter of nearly 5 million mothers who might be eligible for child support actually get it. Most of the ones who don't recieve it end up on welfare and account for 83 percent of the people receiving Aid to Families With Dependent Children. Since the federal government has started pursuing delinquent fathers, the welfare rolls have dropped from 11.5 million in 1975 to 10.3 million last year, but it hasn't been cheap. In 1979, the government collected $1.3 billion from delinquent parents but it cost $365 million to do it.

Some people will object to a federalized approach to child support, saying it is just one more way in which the government is dabbling in private family matters. But government is already dabbling in private family matters when it supports children and chases down delinquent parents.

A lot is going to be made of the Miller story. Some will say the judges struck a blow for equality by throwing a delinquent mother in jail and others are going to wonder why the jails aren't full of delinquent fathers. But the real point of the story is that some women are going to duck child support payments just like some men have, and that the child support system isn't going to work any better when the father is the custodial parent and the mother is supposed to pay than when the situation is reversed.

In that sense, the judges are right in linking the Miller case with the issue of equality. The child support system we have now is probably going to continue working equally poorly, no matter who is supposed to pay.