"Toot one’s own horn” (to promote one’s self) is an idiomatic expression. It has little to do with actually playing horns, but there are jokes.

“I don’t like to toot my own horn but I am very talented at playing other people’s trumpets” was posted on Twitter by thomas on November 2, 2014. “If I were a trumpet player I would constantly borrow other people’s trumpets. I’d hate to toot my own horn” was posted on Reddit—Jokes on January 2, 2016. “I don’t like to toot my own horn, which is why I steal other people’s trumpets” was posted on Twitter by Elijah the Middleborne on February 11, 2020. “I hate to toot my own horn, but I’ve gotten pretty good at playing other people trumpets!” was posted on Reddit—3amjokes on November 19, 2021.


Wiktionary: toot one’s own horn
Verb
toot one’s own horn (third-person singular simple present toots one’s own horn, present participle tooting one’s own horn, simple past and past participle tooted one’s own horn)
1. (idiomatic) To promote oneself; to boast or brag; to tout oneself

Twitter
thomas.
@TStape03
I don’t like to toot my own horn but I am very talented at playing other people’s trumpets.
9:43 PM · Nov 2, 2014·Twitter for iPhone

Reddit—Jokes
Posted by u/[deleted] January 2, 2016
If I were a trumpet player I would constantly borrow other people’s trumpets.
I’d hate to toot my own horn

Reddit—Dadjokes
Posted by u/keithasaurus September 2, 2018
If I were a trumpet player I would constantly borrow other people’s trumpets.
I’d hate to toot my own horn.

Twitter
Elijah the Middleborne
@TheMiddleborne
I don’t like to toot my own horn, which is why I steal other people’s trumpets
10:31 AM · Feb 11, 2020·Twitter Web App

Twitter
bea
@trashwithab
“toot my own horn” is such a stupid expression. like , what other reason would you own a horn if not to play it. do you go around playing other people’s trumpets. but you already have your own it makes no sense
4:23 AM · Nov 30, 2020·Twitter for Android

Twitter
Kathleen McCarthy
@ksmccarthy24
If I played the trumpet, I’d have to borrow other people’s trumpets. I’d hate to toot my own horn.
9:18 PM · Jun 15, 2021·Twitter Web App

Twitter
Jimmy RevJim Olsen
@mybuddyjimmy
If I were a trumpet player I would constantly borrow other people’s trumpets. I’d hate to toot my own horn. #AndNowThis
9:40 AM · Jul 11, 2021 from Des Moines, IA·Twitter for iPhone

Reddit—3amjokes
Posted by u/thomasbrakeline November 19, 2021
I hate to toot my own horn, but I’ve gotten pretty good at playing other people trumpets!