We wear a shirt, a jacket but a pair of pants.
Why is pants plural?
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The site has an entire page on this issue. Here's a brief snippet.
Before the days of modern tailoring, such garments, whether underwear or outerwear, were indeed made in two parts, one for each leg. The pieces were put on each leg separately and then wrapped and tied or belted at the waist (just like cowboys’ chaps). The plural usage persisted out of habit even after the garments had become physically one piece. However, a shirt was a single piece of cloth, so it was always singular.
It actually makes perfect sense. Think of these examples. "The clown wore a pair of pants where one pant was red and the other pant green". Also, "The amputee wore his pants with one pant tied up and the other pant covering his good leg". The proper use of the singular and plural is used to make the meaning clear. Or if you look at panties as a whole with two openings or two short upper leg coverings we use the plural, however, if we only refer to the single toursal opening we say "panty waist", especially when referring to a male who is less masculine or who acts cowardly. And by the way "sleeves" is upper body equivalent of pants. "The shirt has short sleeves". "He wore short sleeves". In both these examples we used sleeves as a noun. When we use it as an adjective of a singular noun, we use the singular, ". . . short-sleeve shirt".
The "proper" phrasing, is more lax than most. Just as you don't have to say "I" at the beginning of sentences that imply the word.
The plural 'pants' is already the plural of pant. Pairs is the word which becomes plural when referring to multiple pairs of pants.
Merely we lazy so grammar has to make an exception for English being a living language and people speaking as they wish. The "pairs of" became implicit in-context.
Pants are accurately representing the plural of pant at all times with a standard "s". A clothing factory may have 999 pants, though we will usually call these "pant legs" due to ambiguous usage.
"Pair of pants" is changed to "pairs of pants" but we do not always say "pair of" or "pairs of"; creating the confusion.
This applies equally to binoculars, socks, glasses and any thing which can be correctly described as "pairs of X" but often occurs abridged.