One of Trump's knacks is to come up with nicknames that define his opponents.  Biden, stupidly, decided to try to beat Trump at his own game. He chose...poorly.

Trump's nicknames usually aren't clever in the sense of puns, rhymes, or pop culture references.  What they do, though, is instantly summon up the worst aspects of the person Trump has labeled.  In Trump's capable hands, nicknames are pure Alinsky: "Pick the target, freeze it, personalize it, and polarize it."

During the 2016 Republican primaries, Trump pretty much destroyed Jeb Bush by calling him "Low Energy Jeb."  It's a bit of a mouthful, but every time Trump said it, he reminded people that Jeb!, even with an exclamation point after his name, was one of the least inspiring people ever on the Republican debate stage.  Even now, if you start typing "Jeb Bush" in the YouTube search bar, the auto-suggest is "please clap":

During the presidential race itself, Trump called his opponent either "Crooked Hillary" or its alternate, "Lyin' Hillary."  Even if they wouldn't admit it, Hillary's staunchest supporters knew that her relationship with the truth was distant at best.  And everyone else in America was reminded that Hillary was extraordinarily corrupt.

By calling Elizabeth Warren "Pocahontas," Trump managed to maneuver the socialist scold, who got herself onto Harvard's law faculty by claiming to be Native American, into taking a DNA test.  The fact that she then proved to be as little as 1/1,024 Native American is still a running joke about that limousine leftist and race-hustler.

One of Trump's nicknames for Biden has been another winner: "Sleepy Joe Biden."  That one has a clever rhyming scheme. "Sleepy" instantly makes everyone think of "creepy" in connection with Biden.  After all, there are legions of videos and photographs showing Biden pawing and sniffing women and girls.  Moreover, to escape the nickname, Biden has to act extra perky, which is a strain for a man who appears to dose off during broadcasts from his basement:

Joe Biden fell asleep during his town hall with Hillary Clinton. To be fair, everyone else watching was also asleep. pic.twitter.com/S4EIzVjA1I

— JT Lewis (@thejtlewis) April 28, 2020

Foolishly, Biden decided that he could beat Trump at his own game.  He therefore proudly announced that he now has a nickname for Trump:

Trump was out there tweeting again this morning. I call him President Tweety.

No, Joe, nooooo!  That's the worst nickname you could have chosen — worst, not for Trump, but for you.  At a basic level, it reminds voters that Trump users Twitter to communicate directly with Americans, bypassing a media establishment that even leftists have to concede is hostile to him.  If Biden had any smarts, he would never remind people to check out Trump's tweets.

At a secondary level, for voters over 30 or so (and there are a lot of them), the nickname "President Tweety" is a reminder of one of the most lovable Looney Tunes characters: Tweety Bird.  

Tweety is a smart, funny, resourceful, and always successful fighter against a stupid but relentless adversary who literally wants to kill him.  Tweety also has a great pop-culture catchphrase: "I tawt I saw a puddy tat.  I did!  I did taw a puddy tat!"

Everyone knows Tweety, and everyone likes that little charmer.  For Biden to choose a nickname that ties Trump to one of the most memorable, quick-witted, and likable characters in American pop culture history is a mistake of truly epic proportions.  It's a mistake perfectly in keeping with a sleepy, creepy, corrupt, and somewhat senile man who wants to be president.