Miguel Cure, 22-year-old new father, proudly carried his 6-pound, 12-ounce daughter, Maria, out the door of Metropolitan Hospital, a place that gives medical care to the poor of Spanish Harlem.

"I don't see why they want to close this hospital," he said. "I think it gives my daughter very good care. Yeah, good care, bien."

But Mayor Edward Koch does want to shut down Metropolitan Hospital and Metropolitan is not alone in its jeopardy.

Inner-city hospitals have been closed or squeezed in size or moved out to growing suburbs recently in cities all across the country -- Philadelphia, St. Louis, Detroit, San Antonio, Wilmington; and others.

The central and inner-city hospitals of America are an endangered species.

They have been hit by the flight to the suburbs of affluent, paying patients and naturally then, their doctors. They are afflicted by reductions in municipal budgets -- New York, of course, is a basket case -- and ever more restrictive, often inadequate state Medicaid payments for the indigent. At the same time, the city poor who can pay nothing for care remain large in numbers.

The inner-city hospital, moreover, is typically a hospital that serves primarily black and brown patients. So the practical effect of its attribution, say many black and brown leaders, is medical rationing by race.

Mayor Koch says New York hospitals, including the 17 in the massive municipal system, have too many expensively maintained beds for today's needs. In Detroit, St. Louis, every place where city hospitals have been slashed away, officials have said the same thing.

But Dr. Alan Sagar, an urban and health planner at Brandeis University, studied 326 hospital closings, relocations and eliminations by merger between 1937 and 1977 in 18 Northeast cities, including Washington and New York. He found that, on the average, hospitals that had many empty beds were actually least likely to close.

The number of closed hospitals was "directly related," however, to a city's percentage of blacks. There is no question, he said last week, but that the number of minority-dwellers in a city strongly helps determine a hospital's fate.

So the closing of hospitals is becoming a new minority cause, Harlem's Democratic congressman, Charles Rangel -- new, strategically-placed chairman this year of the House Ways and Means health subcommittee -- has charged that Koch's hospital-closing plan amounts to "systematic genocide."

Civil Rights and minority groups are fighting Metropolitan's closing. Residents of Spanish Harlem have been parading with posters showing Koch wielding an axe. "Alcalde Koch," the posters demand. "Por que cerrar el Centro Medico Metropolitan?"

Or: "Mayor Koch, why close Metropolitan Hospital Center?"

Indeed, why?

The answer, say New York officials, with officials of other cities in the same boat, is by no means a matter of choosing care for white skins over dark. All groups, they maintain, have joined the flight to the suburbs that has stranded city hospitals. And they can point to Washington's privately owned Doctors Hospital as one that served whites and blacks, yet has had to declare bankruptcy because of the shift of paying patients of whatever hue.

New York City faces a $1 billion budget deficit. Equipped with the recommendations of his health task force, Koch proposed in June to shut down, or all but shut down, four municipal hospitals, the largest of them, Metropolitan. He said closing Metropolitan alone could have $12 million a year.

His medical advisers told him the city's underfinanced, understaffed municipal hospitals often harm rather than help the sick, and the poor could get better care at other nearby hospitals and clinics.

"That's fine thinking, but where are the clinics" said Edward Acosta, Metropolitan Hospital's stocky, crew-cut executive director, last week. "I know of only one private doctor around here. I know of no clinics capable of absorbing the 88,000 prople we saw last year in our emergency room and the 294,000 in our outpatient clinics. The federal government has actually declared this a 'medically underserved area.'"

Medical experts generally agree: good, all-purpose medical clinics could indeed replace many faded hospitals and give better care. But the clinics more often than not never materialize.

That, says Herbert Semmel, a Washington public interest lawyer, is exactly the case in Philadelphia, where the city demolished its old Philadelphia General Hospital. Semmel heads the center for Law and Social Policy, which is involved in legal actions to try to prevent hospital closings in San Antonio, East St. Louis, Gary, Ind., and Wilmington, as well as that of Metropolitan Hospital.

Metropolitan's East Harlem site, at 1st Avenue and W. 97th St., is within a few miles of some of Manhattan's finest hospitals, filled with paying patients. "Ours are 70 percent Medicaid and 15 percent Medicare," said Acosta, "and then 10 or 12 percent 'self-pay,' which means 'no pay.' That's where our deficit comes from."

But the look of poverty is stamped on this hospital and many of its patients. It is stamped on crowded, four-bed wards and gray hallways.

The look is different in a recently renovated children's ward, on one of three floors that have been modernized and divided into attractive semi-private rooms.

"If we can just get $1 million a year for 10 years from the city," said Community Affairs Director Robert Sancho, "we could renovate all our wards to attract many more paying patients, and implement our plan to start a doctors' group-practice clinic. This could turn us around financially."

New York City's Health Systems Agency, its federally financed, strongly autonomous health planning body, this month called Metropolitan a "needed" facility and said it should be kept open to give it this chance.

Koch, it is felt, will probably be forced to take this advice. New York Gov. Hugh Carey backs the hospital. Koch has already suffered the resignation of Deputy Mayor Haskell Ward, his highest ranking black, over the Metropolitan issue.

"But we could stay open and still bleed slowly away," said nurse JoAnne Bennett, the hospital's assistant executive director for maternal and child care.

She gestured toward a set of intensive and special care nurseries for babies in peril.

"This is a good hospital," she said. "We have good nurses here. But we don't have enough of them. And every time there's a city fiscal crisis, there's a new freeze, and we lose a few more.

"We need our public hospitals. We need support here."