Beauty standards.
When we see pictures of women from the twenties, we're seeing photographs or drawn images/painted images. Much like today, more photographs were taken of women considered beautiful than those who weren't, and because taking photographs was much more of an ordeal than nowadays, when they were taken they were of women who generally had prepared for the photograph. That means dressing to change silhouette, but also make-up and hair, both of which were done to emphasise or create the soft, rounded, smooth-faced appearance that was particularly valued at the time. Portrait photographs and movies were lit and shot from specific angles so as to create this appearance, as well.
In contrast, the modern beauty standard emphasises cheekbones and bone structure, so hair is cut to draw attention to those things. The modern standard 'bob' hits at or below the chin, which emphasises the jaw, whereas the iconic 1920s bob hits mid-way between the jaw and the cheekbones and is often carefully curled; this changes the way we see the shape of the face. 'Contouring' makeup techniques are also popular now, which create or darken shadows below the cheekbones and slim the face. This makes it seem like the 'average' face now has a more prominent bone structure than we would see in a vacuum. In the 1920s--this is overly generalised, but works for the purposes of this question--makeup often involved drawing a dark, small mouth, which makes the chin look rounder and softer, and thin, high, curved eyebrows, which soften the look of the brow-bones and, slightly, cheekbones.
Also--and this is only conjecture; I've never seen this studied--photography techniques at the time produced images that had high contrast and were often blurred. This tends to make things like small shadows on the face harder to see, which contributes to that very soft look. Many filters work this way, as a small amount of blur makes blemishes much harder to see and evens out skin tone.
As for drawn and painted images, they were very often idealised in the process of production, again to match that ideal appearance that was the goal at the time.
Edit: I posted some sources further down the thread in response to a comment which is now deleted; for visibility, since this answer is getting much more attention than I'd expected, I'm putting them here as well:
This article talks a lot about the rise of popular photography and where and why photographs were being taken, and of whom: https://omnilogos.com/photography-and-society-in-20th-century/ but it doesn't quite make the link to beauty that I've put forward here. It has interesting notes about photography and advertising.
There's more good stuff about photography here, although it focuses on artistic photography: https://smarthistory.org/an-introduction-to-photography-in-the-early-20th-century/
This is a couple of contemporary guides on applying makeup, which is very brief but interesting: https://hair-and-makeup-artist.com/1920s-makeup-colours/
'Fashions in Makeup: From Ancient to Modern Times' (R. Corson, 2004) is a much more comprehensive history of cosmetic trends. If you can get it in a library, have a look.
This is a good overview of illustration in advertising in the early 20th century and shows a lot of the kinds of idealisation and stylisation of figures that I've talked about: http://www.vam.ac.uk/content/articles/f/fashion-drawing-in-the-20th-century/
And this Library of Congress online exhibition puts together plenty of examples: https://www.loc.gov/rr/print/swann/beauties/beauties-exhibit.html
Edit #2 to say that a bunch of helpful redditors have shared some more specific examples and discussion in the comments, scroll down! Great work, team :D