Why does it keep saying I need a software update when I connect my iPhone 11 to my MacBook Pro?

You plug the phone into the Mac again, and when the Mac tells you the Mac needs a software update, you suspend your disbelief and follow through with the update on your Mac.

If you never plugged your phone into your Mac, both would be completely up-to-date, as reported.

<< says it is unable to update >>

Try the same process in Safe Mode, where no third-party add-ons can interfere with the software update process.

Start up your Mac in safe mode - Apple Support

.

If you see "Software update is required to connect to your iOS device" on your iPhone, iPad, or iPod touch - Apple Support

.

Exactly the same problem, and Safe Mode doesn't change anything : when I plug my iPhone by USB to my iMac, I have the same boring window… It's obviously a bug. My marvelous iMac 27' late 2013 works well after nearly a decade (with a SSD in place of the fusion drive), but I can't hope an OS update : I stay at Catalina for eternity ! And so this bug :) ?

Please read this Discussion for a description of the problem and the workaround that solves it:

"Your iPhone needs to update software to connect to your Mac"

That advisory has a link to the update:

The file is small and simply patches iTunes on macOS 10.14 and older so it can work with the new iOS version. It will NOT change you computer's macOS version. I get it on my Mojave 10.14 Macs every time a new major upgrade oof iOS or iPad OS comes out.

With certain combinations or modern MacOS and modern iOS, your Mac needs a software update to communicate properly with the phone. It is not an accident that is when it alerts you.

It's the Mac that needs the update, not the phone.