My Mac OS is High Sierra but the newer ones aren't showing up as compatible updates. Why can't I update to the latest OS?

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

Computer Qualify for the Monterey upgrade

macOS Big Sur 11 hardware requirements

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

macOS High Sierra 10.13 hardware requirements

Caution - jumping over all the newer versions and directly to Big Sur  / Monterey on Qualifying computers is Technically possible - there are those who have attempted and were successful. Then there are those who attempted and had less than good results.

If this is a Production or Mission Critical Set-up - a more prudent and measure approach is suggested. 

The above is from observations on the Apple Support Community Forums and IMHO

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

This could be a MBP 2013 or MBP 2014

If correct these models qualify for Big Sur macOS 11

• MacBook Pro (Retina, 15-inch, Mid 2014)
• MacBook Pro (Retina, 13-inch, Mid 2014)
• MacBook Pro (Retina, 15-inch, Late 2013)
• MacBook Pro (Retina, 13-inch, Late 2013)

Please tell us exactly what model Mac you have.

Go to Apple > About This Mac. What does it say for Mac, Processor, Memory & Graphics?

Go to Apple > About This Mac > System Report > Hardware. Under Hardware Overview, what does it say for Model Identifier?

If you post any screenshots, please remove your serial number from the image.

That is because one has not actively sought out any upGrades beyond what this computer may have come installed with.

Understand, High Sierra was released in 2017 and there have been several newer version available for upgrading to since that time.

The Update feature was only introduced in Mojave macOS 10.14 and above so it is a fault of the OS or defect.

Now, one has been offered a possible solution and means by which the computer can be upGraded up to and including possibly Big Sur macOS 11 released in November 2020