1. The things housed by a bra give out a single type of output, the
things housed by panties give two different types of outputs
2. In the product evolution history, the bra was initially formed by
a single piece of fabric (a kerchief, actually. In India - a
kanchuki), while panties were initially formed by two different
pieces of fabric joined by a string.
3. the two breasts are basically the same stuff - simply mirror
images. The nether regions housed by panties are of course not mirror
images or something - they are different organs.
4. a bra can be rightfully worn by ONE single gender - the ladies. A
panty can be worn by BOTH genders (re: David Beckham and other such
kinky characters)
5. Panties is plural simply because it is a short-form of
pantaloons/pants - perhaps early panties were truncated
pants/pantaloons?
Now, here's a very possible explanation - hear me out
The word brassiere is connected with "woman's underbodice," from Fr.
brassière "child's blouse or shoulder strap" (17c.), from old French
braciere: arm guard - from bras "an arm," from Latin brachium.
So, the origin is really the arm guard, as something to brace one's
shoulders - a military origin of the word. Now, the arm guard was
worn by male soldiers as well as the female soldiers, correct? For
the male soldiers, the arm guard was on only one side anyways - hence
the singular form of the brassiere is valid here.
Now comes the interesting part - the female soldiers, and their arm-
guards/braces/brassiere
Which is the most popular historical genre of female soldiers? The
amazons, of course. What is the legend of the amazons? That they were
fierce soldiers and, interestingly, had a practice of cutting off one
of their breasts, so that they could draw the bow-string fully
without being hampered by their breast. Obviously, their breast
guard/brace/shoulder strap would be singular, since they had to brace
only one breast. (did you know that the word amazon etymologically
means "having only one breast" (a- "without" + mazos "breasts)? ).
Ergo - the brassiere is singular, and panties are plural