Y'see, here's the problem... you haven't provided the example so your question is meaningless.
Trousers
A euphemism is a nice way of saying something... It all depends on what your "other words" are, and in many cases if there is one euphemism for something, there are also several more.
A euphemism is a word that is meant to imply another in a way that is slightly less harsh or direct. One euphemism for prison, jail, rehabilitation center or penitentiary could be "pen."
The euphemism for "criminal" could be "wrongdoer" or "offender."
Peculiar can be considered a euphemism for the other three, so that means one of the other three would not be one.
Trousers
peculiar
loathe
lie
A euphemism is a polite, socially acceptable way of naming something else. For example, a public toilet being called a "comfort station", or "Sailsbury steak" as a euphemism for a hamburger.
No. It is a figure of speech. A euphemism is a word substituted for another word that is deemed unacceptably explicit. For example, the word mortician came into vogue as a euphemism for "undertaker," which was considered too direct and to the point.
To accurately identify which word is not a euphemism for the others, I would need to know the specific words in question. Euphemisms are generally used to soften or rephrase terms that may be considered harsh or unpleasant. Please provide the list of words you're referring to, and I can help you determine which one stands out.