Older browsers lacking certain APIs / features.
E.g. let’s say you want your app to use WebUSB to interface directly with a USB device. Oh wait, can’t use that, Firefox and Safari don’t support it yet.
Developing web apps can be a pain when you’ve got numerous browsers with different web standards implemented to varying, inconsistent degrees. Compound that with supporting older browsers and you’ve got a web apps not able to leverage modern features and suck using lowest common denominators.
Honestly, browsers are the most dangerous membrane through which we let untrusted code permeate. One really shouldn’t be running old versions of browsers with unpatched vulnerabilities residing in them. I don’t see the problem in any web service ending support for browsers that are >6months out of date.