As the title says. Just curious, this has been an ongoing joke along with Donald Duck and Pooh not wearing pants but when they bathe they put towels on their waists.
Part of the answer has been placed on the iconic look of the strong man from the circuses of the 1920s and 30s. But there was another answer that lies in the process used to print comic books in times of yore.
The process used was called offset printing. Offset printing was actually invented by accident in 1903 by Ira Washington Rubel, but it didn’t really gain steam until the 1940s. (It gained even further popularity in the 1950s due to improvements in ink, paper and plates.)
According to Wikipedia, “Offset printing is a commonly used printing technique where the inked image is transferred (or “offset”) from a plate to a rubber blanket, then to the printing surface. When used in combination with the lithographic process, which is based on the repulsion of oil and water, the offset technique employs a flat (planographic) image carrier on which the image to be printed obtains ink from ink rollers, while the non-printing area attracts a water-based film (called “fountain solution”), keeping the non-printing areas ink-free.”
This is a large scale 4 color printing press. Product goes in on one end and each color is applied in turn.
It’s very easy to tell if something has been created using offset printing. If you look at a newspaper and see a page that has images where they don’t quite seem to line up, that is because one of the printing plates was a little off when they were laying down a color. It is still in use today and is a great way for printers to make cost effective prints. If you look at Golden Age heroes you notice that all of them tended to wear costumes that were designed with alternating colors. Printing was done on large presses and as pages were printed with inks being fed onto pages one four color ink at a time (cyan, yellow, magenta and black).
All-Star Comics Vol 1 #36 August, 1947
Large print runs would have to check to see if the pages were slipping as they were printed. This slippage would cause the pages and colors to be out of alignment. Since supers were brightly colored, it was easier to check if a page was aligned by using the alternating colors of the characters as "registration" markers. Gloves, briefs, and boots were the reference markers used to ensure characters were maintaining their alignment on a page as a print run continued. Part of the technology used paper plates, which were known to slip out of alignment as the print run continued.
While more fanciful answers are often more interesting, the actual reason for many early character costumes can be summed up to a physical limitation in the process used to produce the books they were printed in.
DC Officially Confirms Superman Didn't Wear Red Underwear (Inverse Magazine)
In a recent issue of Action Comics #967, Superman reveals his "underwear" weren't underwear at all. Instead he claims they were a decorative element sewn onto the tights, emulating strong-men outfits of the time period.
This allowed DC to upgrade the Pre-Flashpoint Superman to redesign his costume to resemble a variation of the Post-Flashpoint Superman's costume design minus the Kryptonian armor.
During the 1930s it was common for superheros to wear scape outfits and mythology based gear. Many of these superheroes wore shorts outside their suit, which soon became a trade mark of all future superheros.
Superman is a pioneer of this outbreak.
There is also a theory about comic book characters being drawn that way in general, because it added more color.
The pair re-envisioned the character, who became more of a hero in the mythic tradition, inspired by such characters as Samson and Hercules, who would right the wrongs of Siegel and Shuster's times, fighting for social justice and against tyranny. It was at this stage the costume was introduced, Siegel later recalling that they created a "kind of costume and let's give him a big S on his chest, and a cape, make him as colorful as we can and as distinctive as we can."The design was based in part on the costumes worn by characters in outer space settings published in pulp magazines, as well as comic strips such as Flash Gordon, and also partly suggested by the traditional circus strong-man outfit, which comprised a pair of shorts worn over a contrasting bodysuit. However, the cape has been noted as being markedly different from the Victorian tradition. Gary Engle described it as without "precedent in popular culture" in Superman at Fifty: The Persistence of a Legend. The circus performer's shorts-over-tights outfit was soon established as the basis for many future superhero outfits. This third version of the character was given extraordinary abilities, although this time of a physical nature as opposed to the mental abilities of the villainous Superman
According to Action Comics #967, the red 'trunks' weren't a separate piece of clothing that went over the supersuit, they were a ...
... that was an integral part of the suit itself. So the very short answer to your title question is "He doesn't".