Through all three of those centuries, people spoke out against corsets as physically damaging to the female body. In the late sixteenth century, the French surgeon Ambrose Paré was doing autopsies that showed the characteristic overlapping ribs caused by tight-lacing, and he claimed that a young bourgeois woman had died in 1581 from being laced too tightly and eating her usual amount of dinner; Michel de Montaigne, his contemporary, wrote that women suffered tortures and died from trying to obtain a very slender, "Spanish" body. John Bulwer wrote in The Artificial Changeling (1653) that young women

reduce their Breasts into such streights, that they soon purchase a stinking breath; and while they ignorantly affect an August or narrow Breast, and to that end by strong compulsion shut up their Wasts in a Whale-bone prison, or little-ease, they open a door to Consumptions, and a withering rottennesse.

Criticisms of corsetry on medical grounds continued on much the same lines for as long as women kept wearing them, blaming women's decision to wear them for cancer, scoliosis, liver lobes, gallstones, birth defects and miscarriages, and basically any physical or mental complaints that women had, particularly if said complaints were more prevalent in women overall. John Leighton's Madre Natura Versus the Moloch of Fashion (1874) collected all of the conditions said to be produced by the corset:

In the Head

Pains in the head

Sleepiness

Bleeding at the nose

Flow to the mouth and lips

Giddiness

Apoplexy

Pains in the eyes

Ear ache

Stoppage in the nose

Tendency to fainting

Obliquity of vision

Swellings in the neck

Carotidean aneurisms

In the Chest

Sores on the chest

Hooping cough

Abscesses in the lungs

Polypus

Water on the chest

Displacement of the bones of the chest from their situation

Impediment to the action of the lungs

Impediments in the action of the heart

Depression of the lower bone of the sternum

Hunchback

Pain in the region of the heart

A false support given to the thorax and the development of a real support impeded

Inability to suckle in consequence of pressure on the breasts

Cough

Schirrhus in the mammary glands and ultimately cancer

Adhesion of the lungs to the diaphragm

Asthma

Disturbance of the circulation hence inflammation &c

Short breath (dyspnoea)

Spitting of blood

Cavities in the lungs

Consumption

In the Abdomen

Disturbance of the functions of the diaphragm

Pressure on the stomach

Hence pains in the stomach

Loss of appetite

Sickness

Acidity

Vomitings

Vomitings of blood

Bad digestion

Scirrhus of the stomach

Flatulency

Diarrhoea

Adhesion of the intestines

Induration of the mesenteric glands

Colic pains

Tenesmus

Haemorrhoids

Fistula in ano

Dysentery

Hypochondriasis

Compression and obstruction of the liver

Jaundice

Inflammation of the liver

Hardening and suppuration of the pancreas

Diseases of the spleen, inflammation, suppuration, and scirrhus

Diseases of the kidney

Calculi

Strangury

Hernia of the bladder

Bloody urine

Hysteria

Disturbance of the catamenia

Leucorrhoea

Hardening of the ovaries

Inclination of the mouth of the uterus towards the sacrum

Scirrhus of the womb

Haemorrhage from the uterus the separation of the placenta

Sterility

Unhealthy children

Ugly children

Monstrosities

Miscarriages

Premature labour

Difficult labour

Protracted labour

Adhesion of all the viscera of the abdomen

Disfiguration of the viscera

Dropsy of the belly

Hernia

Swelling of the upper extremities

Swollen feet

General Diseases

Pains

Want of energy

Melancholy

Flying heats

Intermitting fever

Eruptions

Chlorosis

Atrophy

Epilepsy

Tending to disease of the bones

Sickly and short life

Man! That's a lot! But the thing is ... historical medical science was not exact, and without the theories and tools that we take for granted now the mindset of doctors and researchers was quite different. I wrote about the perception of consumption/tuberculosis in the eighteenth and nineteenth centuries last week: they did not know that germs existed, and they did not know why some people were more susceptible than others to certain issues. Today we know that epilepsy and depression are neurological conditions, dysentery is caused by various pathogens, asthma has genetic and environmental factors, and there are no studies that show that the many vaguer complaints listed above can be traced back to the corset. Yet it is assumed by most today that these are actual effects of tight-lacing, despite the fact that if you suggested leeches or bloodletting or tinctures of silver nitrate or mercury to help medical conditions - cures considered appropriate in the eighteenth and nineteenth centuries by many of the same doctors who railed against corsets - modern people would, for the most part, cringe and laugh and talk about how crazy medicine was back then. There has only been one study about the physiological effects of corsets, which shows only issues of shortness of breath, and while it's fairly flawed (it's silent on the methods and patterns used to make the corsets, and I'm suspicious that they were not made in a period way for optimum fitting) it also shows that the women who had shallower breathing while tight-laced were not seriously bothered by it or prone to fainting.

The reason doctors were so likely to ascribe women's health problems to corsetry, other than the fact that certain complaints are more prevalent in women and would therefore seem to be caused by some environmental issue specific to them, is that corsets were seen as an expression of vanity. The narrative was, essentially, "women are so vain that they've got to have tiny waists even though it kills them and their babies." The frontispiece of Madre Natura celebrates the unlatered female form, while the title page shows two harpies labeled "Fashion" and "Vanity" pulling the laces on a wasp-waisted corset above the motto "A la Mode - A la Mort" (Fashionable to the Death). A third image draws a rather tasteless comparison between American chattel slavery and fashion with the caption "Am I not a woman and a sister?" and a fourth shows a corseted woman with vipers coiled around her waist, threatening to bite her. As with the consumption issue in the previous answer I linked, it helped people to make sense of the deaths and medical problems around them to have something concrete to blame, in the absence of our current understanding of pathogens, debility, and anatomy, and the connection between women and destructive vanity was much older than corsets and stays. Even dress reformers, who were typically feminists/women's rights activists, played into misogynistic themes by assuming that women could not be interested in both fashion and education, or chose to wear corsets at the cost of their lives in order to be pretty. In reality, by the late nineteenth century, most women in Britain, France, and America at least were wearing corsets on a regular basis with no ill effects, and because of their own experiences, they took what they were told by anti-corset crusaders with a grain of salt. We can tell with experimentation today that corsets mainly move body fat around, rather than crushing organs, and that the overlapping/reshaped ribs of a tight-lacer do not tend to cause medical problems; heartburn and burping do seem to be issues if eating a sizable meal while corseted, but these are not life-threatening problems.