Is there a more polite idiom for "comparing whose penis is larger"?
Solution 1:
Credit to user576 for their comment.
I've searched the web for "let's not compare whose penis is larger" and got no results, which led me to believe it's not really idiomatic. If you cut it down to "whose penis is larger" you get 717 results, compared to almost 1400 if you search for "whose penis is bigger", which really sounds more natural.
There is, however, a vulgar equivalent to "let's not compare whose penis is bigger", namely, "let's stop this pissing contest".
A pissing contest is any argument that just goes back and forth between two individuals but never gets resolved. - The Urban Dicionary
from Wikipedia — A pissing contest, or pissing match, is a game in which participants compete to see who can urinate the highest, the farthest, or the most accurately. Although the practice is often associated with adolescent boys, women have been known to play the game, and there are literary depictions of adults competing in it. Since the 1940s the term has been used as a slang idiomatic phrase describing contests that are "futile or purposeless", especially if waged in a "conspicuously aggressive manner". As a metaphor it is used figuratively to characterise ego-driven battling in a pejorative or facetious manner that is often considered vulgar. The image of two people urinating on each other has also been offered as a source of the phrase.
- The conversation between the two men was merely a pissing contest, both were trying to impress the attractive woman standing nearby with their wit and intelligence.
Urban Dictionary's crowdsourced definition describes the term as being used figuratively "to refer to a meaningless though nonetheless entertaining act in which people try to outdo one another in any way." Comments found there also describe pissing contests as literal competition "in which two or more people, usually (but not exclusively) male, urinate with the intention of producing the stream with the greatest distance."The New Partridge Dictionary of Slang and Unconventional English separates its definition of "pissing match" (a conflict involving "unpleasantries") from "pissing contest" (a conflict with negative attacks made by both sides). For "pissing contest" it offers a different image from other reference works: "From the graphic if vulgar image of two men urinating on each other". Both phrases are said to originate in the United States.
Your second question is about a less vulgar way to phrase the same idea. I couldn't find an idiom for it and I therefore suggest "Let's stop this pointless, meaningless or purposeless discussion".
Solution 2:
megalomania or phallic megalomania :-)
Solution 3:
TL;DR: The polite term I'd use for the disruptive cycle of "mine is bigger", "no, mine is bigger" is one-upsmanship.
I often hear of references to a dick-sizing contest (verb form: dicksizing) when people are bragging about whose (something) is the biggest or the best. (I've never heard the word used about guys comparing actual genitalia, just the implication that the comparisons of possessions or experiences are a surrogate for that crude endeavor.) E.g.: Reddit thread of people comparing/bragging how many dirty dishes they build up in a restaurant shift. or LiveJournal post disparaging some measures of poverty
This is not quite the same thing as dick-waving, where people are making idle threats to prove their machismo, (This article about nuclear weapons appears to mix those two concepts) and very different from a pissing contest where people are taking turns blaming, insulting, or damaging each other.
Customer: your software upgrade broke my database.
Tech: You didn't follow the upgrade instructions.
Manager: Let's not get into a pissing contest, let's just fix the problem.
But none of these terms are suitable for polite company.
Some terms I might use:
one-upsmanship -- where people need to top every story or brag with something bigger or more noteworthy.
the art or practice of outdoing or keeping one jump ahead of a friend or competitor (m-w.com)
an effort to show that you are better than someone you are competing with (Cambridge dictionary)
the art or practice of successively outdoing a competitor. (Wikipedia)
bragging rights -- After you've won some such contest, you can boast about how yours is best. (dictionary.com)