Obviously there's a long standing belief that as we move forward in time fashion has become more convenient and independent for women. We've set aside corsets in favor of bras, shorten skirts, started wearing pants, etc. Some of these have tied in directly with the feminist movement, such as the "bloomers" of the 19th century (thanks to Amelia Bloomer) and later garments like the cycling suits of the 1890s. At the time they were worn they were seen as specifically challenging the status quo and in the case of the outfits for bicycling, allowed women the freedom of movement wanted.

In other cases, it's our modern view looking back that has attributed the fashion to feminism. Such as the corset. We (as a society) look back now and think about how restrictive that must have been and assume they thought so as well, therefore the removal of such a thing must have been some sort of freedom just like the bra burnings of the 1970s. In reality, corsets were mainly there to provide back and chest support. The added benefit is that they smooth the figure and that means you can eat that extra piece of cake and not go to the gym to get rid of that fat roll. Women were not, on the whole, complaining in great droves about the discomfort or restriction of the garment. Much of the misinformation comes from ad campaigns by male "doctors" (very loose use of that word) who claimed it caused all sorts of medical problems. In reality, there was (and still is) no proof of those claims and for the most part the group was acting with the belief that corsets were worn by vain women and were too indulgent and focused on appearance.

The move away from corsets in the 1910s was a fairly natural evolution. The corset style had dropped down to below the bust line, and many women needed extra assistance for their chest. These are fairly similar to brassieres, though the early garments called that are more of a bandeau style. As the fashionable figure became straighter, there wasn't as much of a need for these smoothing undergarments. Many older women continued to wear them, not just for appearance, but as back support and the fact that they just felt "normal". Going from never wearing shoes to always wearing them or vice-versa would be awkward at first in much the same way. The biggest proof that corsets were not considered the torture devices we now think of them as is the revival of structured undergarments in the 1950s. Of course, now they're made of elastic and other materials that focus more on pulling in, shaping, and smoothing rather than any actual support. Having worn numerous different time periods of garments, I find that these pieces that our older generations still remember wearing and compare to corsets, are far more uncomfortable than 18th or 19th century true corsets. These again went out when the straight figure of the 1960s came in. It wasn't feminism, but the fashionable shape that killed the corset.

I've seen just about any piece of women's garments attributed to the male desire to keep them from being fully functional. Everything from heeled shoes (originally worn by men), to bustles and crinolines, skirt lengths, and even what side garments button on. It's all unprovable and specious at best. In reality, women have been making (and designing) women's clothing since the late 17th century. Prior to that it was controlled by male tailors. You would think if women had such a problem with the current state of fashions restrictions there would have been a massive revolution when the seamstresses and mantua makers were allowed to form their own guilds and take over much of women's clothing. But there wasn't. Clothing was custom made for each person until the 19th century, so everyone had a say in how their clothing fit and functioned. Petticoats were often at practical lengths (3-5" off the ground in late 18th c. was normal for fashion), and if it was needed for working in they were often shortened more. If you needed more arm movement, you simply asked for it when having the sleeves set.

In reality, the more subtle changes (as far as a lay person is concerned) are far more telling of the cultural changes women have undergone. There's a lot of evidence that when women are being pushed more towards family/home their clothing is more feminine, and vice-versa. The difference between the 1920s and 1950s is a huge example of this. Looking at your flair, the change from the 1920s into the 1930s is an interesting example as well. This was actually a fairly conscious change in fashion (though not abrupt). At the end of 1929 there was a competition in Germany to depict what the woman of the 1930s would be like. Most submissions were consistent with what the last ten years of progress had shown. However, what won was an image much closer to the propaganda we were to later see. A very soft, traditional German girl compared to the harsh, masculine look previously seen. This, of course, did not change the path of fashion by itself, but was indicative of the inspiration sources the 1930s would pull from. Soft ruffles, lace, chiffon, and figure clinging bias cuts are rather at odds with the geometric shapes and dropped waist of the 1920s.

There's also theories that the hemline and conservativeness of women's clothing follows the economy/employment. The 1930s hem dropped severely with the Depression, it goes up to just below knee length in the early 1940s (America was actually doing well then), back down a bit in the 50s, up in the late 60s, down in the 70s, etc. Even today going down from the mini-skirt revival of the late 1990s to modern day around knee-length (or even maxi-skirts). This would be, again, tied in to the theory that as our economy goes down there's less indulgence and more emphasis on returning to the family.

The historiography of fashion is not something that's been looked at widely, as far as I know; right now, we're still mainly in the phase of straightening out the simplified histories often presented during the 20th century, rather than looking at the factors that led to these narratives. But in looking at these old secondary sources as primary sources of their eras' attitudes toward historical fashion, what I see is overwhelmingly a need to create a narrative of progress. (To be honest, this still goes on to a great extent today, but it's not quite as widespread.)

Essentially, people would look at the fashionable figure of the earlier end of the 19th century and then the fashionable figure of the beginning of the 20th century, and construct a story in which A gradually became B. Start with a light, unboned, cylindrical corset, and add more cording in the 1820s - that makes the waist tighter. Add metal grommets in 1829 - that makes the waist tighter still. Add a front-opening split busk in the 1850s - that makes the waist even tighter. Etc. And then, the story goes, women stopped wearing corsets after WWI, coinciding with, according to the narrative, the worst corsets of all. In reality, I haven't found a gradual decreasing in waist size of 19th century corsets, and we must also remember that the corsets worn in the 1910s focused on the stomach and hips rather than the waist, foiling the idea that the corset finally grew bad enough for women to revolt against en masse.

The association of historical corseting with societal oppression is an old one - some 19th century writers believed that Catherine de' Medici introduced iron corsets designed to give every woman at the French court a 13" waist, fitting with a tradition of depicting herself and her son as tyrants with unnatural tastes. In the early 20th century, it was also very common to depict the 19th century as unnaturally oppressive in contrast with a present that was perceived as freer. (See Modern Sexuality and the Myth of Victorian Repression.) Many equated the physical restriction of a corset with the social restriction men imposed on women. Marianne Thesander wrote, strongly, in The Feminine Ideal in 1994:

The corseted female body of the 1800s was the image both of middle-class self-discipline and of a restrictive sexual morality, which literally locked women into a role in which it was almost a duty to be attractive. Their beauty and dress made them into 'valuable' and visible signs of their husbands' wealth ...

[Way harsh criticism of art historian David Kunzle's "fascination" with the corset.] Kunzle wonders why women have voluntarily inflicted on themselves the kind of pain that this constriction of the body causes. 'Are women masochists?' he asks. The answer is that of course women do not have a particular predisposition to masochism, nor do they welcome the pain of being trussed up in a corset; this is one of the many myths about 'the nature of women'. But they have been obliged to conform to the moral and aesthetic norms of the day.

This was and to a vast extent still is the predominant view of corsets in feminism, and to a similarly great extent is influenced by the medical polemics described by /u/colevintage, popular culture (e.g. Elizabeth Swann, Scarlett O'Hara - the number of times I've been talking about actual 19th century corsetry and have been answered with That Scene from GWTW ...), and no experience at all with historically accurate costume corsets. There is also a fascination with noting tiny waist measurements in extant antique corsets - 20-22" - without paying any attention to the equally tiny bust measurements - generally around 30" - which gives the impression of an average-sized woman being tight-laced into a few handspans. And I should mention misleading newspaper articles, such as the one in the Daily Mail which took Lily James's statement that she had soup for lunch before filming the corseted ballroom scenes in Cinderella as solid food made her burp, and turned it into "Lily James was forced to subsist on soup to fit into her corset!" I don't know that I'd say this has influenced feminism, as oppression through clothing really didn't become a mainstream feminist issue until after the corset had been left off (many suffragists made a point of dressing fashionably to emphasize that they were normal women who wanted a voice in government); it's more that the narrative has been useful as an illustration of patriarchal power.

The rise of third-wave feminism has correspondingly seen an improvement in the status of the corset. Museum at FIT director Valerie Steele has done a great deal to promote a view of the corset historically as both a means for women to construct their identity and an undergarment without health risks; poor David Kunzle has focused mainly on the former, not questioning older impressions of the latter. This has become, if not the majority view, then the louder one of the 21st century, so far.

Unfortunately, when it comes to fashion, there is a LOT of misconstrued to down right wrong information out there in current feminism. You mention the corset - yes, some people did tight waisting in the 19th century. However, men wore corsets sometimes as well to get the fashionable figure. Also, the average corset will take you down 3" to 4". Most extant gowns from the Victorian age have a waist of 24" to 26". This means most ladies were a 27" to 30" waist - or your average size 8 to 10 today. In the USA, the average size is a 12 - so not too terribly much smaller.
Today, ladies will take out ribs (Demi Moore), have liposuction, and yes, still wear corsets to make themselves look thinner. The corset hardly seems to be the issue when that can be taken off and doesn't involve a medical procedure! Some modern feminism looks at the corset as a constricting device developed by "men" to keep women in line. This simply doesn't ring true. First, as I've stated, some men wore them too. There are ads from the late Victorian period showing men's corsets right along the women's. If corsets were meant to keep women "down", then why would they be shown for men? The truth is that a good corset will keep everything where it should be. No tummy over the waistband (something many women and men have an issue with now), no low hanging boobs, and it forces the garments to actually lie flat and behave (no popping buttons!).
If any fashion trend is truly to be decried and ridiculed through the lens of modern feminism, it should be the foot binding practices of China that lasted for 1000 years until the 1930's. That truly was meant to keep women from being able to do things (like running or even really walking). The Chinese would break the foot of a three year old girl in three places - the heel, the middle of the foot, and then the toes. The toes were folded under the foot and then the foot was pushed up towards the ankle at the middle, the heel was broken as well to form the new "smaller" foot. This was so to show that the family was well enough off that the girl didn't have to work - and became so ingrained in the society that at her wedding, a girl's future mother in law would look under her skirts to make sure she had tiny feet. If she didn't have the "lotus blossoms", the mother in law would throw down the skirt and could refuse the marriage.