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Soylent Green (1973) takes place in the 2040s and the population has become so great that they used up all the foodstuffs on Earth. Starvation is rampant so a company creates an edible product called Soylent Green

SOYLENT GREEN IS PEOPLE

If all people are being fed a huge amount of the population must be killed, not just a few people, so if a large amount of people must disappear why is the population still so dense?

Film

In the film, the books that Sol acquires (catchily titled "Soylent Oceanographic Survey Reports I+II") show that there has been a recent collapse in food supply from the oceans. In response to this disaster and the inevitable food riots, we learn that a new foodstuff called Soylent Green has started to become available. This is replacing the existing food supplements; Soylents Red, Yellow and Blue which we see in the market scene and which are presumably made from seaweed (the source novel refers to them as "weedcrackers").

Richard: [TV announcer] ... is brought to you by Soylent Red and Soylent Yellow, high energy vegetable concentrates, and new,
delicious, Soylent Green. The miracle food of high-energy plankton
gathered from the oceans of the world.

... (later)

Det. Thorn: Ocean's dying, plankton's dying ... it's people. Soylent Green is made out of people. They're making our food out of people. Next thing they'll be breeding us like cattle for food. You've gotta tell them. You've gotta tell them!

It's not ever made clear whether Soylent Green consists solely of ground-up people or whether it's simply being mixed with the existing seaweed protein to bulk out the new tablets but you can see that the other Soylents are being sold at a huge discount, presumably because their protein count is very low and has been padded out with inedibles.

My interpretation is that this was a stop-gap solution to the population becoming increasingly violent rather than a sustainable solution to feeding the populace over the long term. At the end, when the reveal is made, the likelihood is that it will lead to the collapse of the existing order but possibly also a toppling of the elite who evidently get to eat steak and drink milk.

Novel

The novel on which Soylent Green is based ("Make Room! Make Room!" by Harry Harrison, 1966) is explicit that the reason for the overcrowding is simply that they've projected the current birth and death rate trends forwards into a 'near future' world where 7 billion people live cheek-by-jowl.

"In 1950 the United States—with just 9.5 per cent of the world's
population—was consuming 50 per cent of the world's raw materials.
This percentage keeps getting bigger and within fifteen years, at the
present rate of growth, the United States will be consuming over 83
per cent of the annual output of the earth's materials. By the end of
the century, should our population continue to increase at the same
rate, this country will need more than 100 per cent of the planet's
resources to maintain our current living standards. This is a
mathematical impossibility—aside from the fact that there will be
about seven billion people on this earth at that time and—perhaps—they
would like to have some of the raw materials too.

In the book, there's no "big reveal" at the end. There's simply too many people and not enough food to go around, especially amongst the poor. It's a typical overcrowded dystopia.

The movie depicts 40 million people residing in New York City alone, which is extremely high, yet one could reason the population may have been even denser prior to Soylent Green production. In addition, hungry people may be flocking to New York City from depopulated rural areas to find food.

The movie does refer to other sources of food being scarce but not completely absent (indeed the elite enjoy meat and fresh produce), and that resorting to cannibalism of the elderly is a deperate ploy by the authorities to feed an overpopulated Earth (and perhaps a grim solution to reducing the world population).

BTW this question was investigated in this 2011 article, with the finding that cannibalism is not a viable long term solution to maintaining the human population:

Those victuals translate into about 60,000 kilocalories. Humans need 2,000 to 3,000 kilocalories a day for sustenance. (The "calories" listed on nutritional labels are actually kilocalories.) Assuming there was barely enough chopped-up man-meat to go around and the cannibals were getting only 10 percent sustenance per day based on a 3,000-calorie diet, a single person could provide 200 days of sustenance to the person who eats him.

Even so, Vogel writes, "a population would have to sacrifice nearly two of its adults each year for each of its (surviving) members. That means [the population] would decline by almost an unthinkable two-thirds each year."

The population seems "dense" because there is a scarcity not only of real food, but also of jobs, shelter, etc, that would give the impression that there are too many people if there wasn't a problem of overpopulation to start with.

I don't know if you are just talking about the movie or want to discuss also the original novel by Harry Harrison.

If I recall correctly, people are not really killed

specifically to make Soylent Green,

although an "euthanasical" form of suicide is encouraged by the government

and the bodies go the described end.

There are also some other "ingredients" in the Soylent Green (probably some of the ones used for Soylents Red and Yellow), that would make a little bit more viable that "production" system. Not that is sustainable, of course. Also remember that that kinds of Soylent are still produced.

Soylent Green is more a patch than a solution. If population in this story is to reach something close to equilibrium, it will be by the starvation of thousands (that will be used for you know what), and still won't happen any time soon.

It's mentioned in the movie that Soylent Green is a fairly new (and popular) food product. Soylent Green isn't the only food source, it's a new addition to the existing - and increasingly inadequate - food sources. It's shown in-universe (more-or-less) that it's highly processed, so it's presumably sterilized to avoid the bacteria and viruses ("germs") that long pig can carry. One of the major downsides of cannibalism is increased risk of infection - many germs are species-specific. It's worth noting that prion diseases weren't well understood at the time the book and movie were made, but science-marches-on.

My guess is that institutional cannibalism isn't meant to be sustainable; it's meant to serve the dual purpose of reducing the population while also feeding the ones remaining.

For further reading on this delightful subject, I recommend Harry Harrison's Make Room! Make Room! (1966), Jonathon Swift's A Modest Proposal (1729), and Anthony Burgess' The Wanting Seed (1962). There are lots of other examples, it's a fairly common trope.