Your CS teacher never looked at a web browser from the inside, or at other actual big scale software.

Still, the teacher is right for most user-facing software that most of us will ever write.

I'm not convinced. If designing the features and interface weren't so challenging, why do the user interfaces and other development APIs to web browsers still change 30 years after they were first invented?

A web browser might have a higher density of advanced algorithms (than most software, but only because it has unusually extensive, varied and complex requirements (e.g. a number of complex standards like HTML, JavaScript, CSS, WebGL) and unusually high quality standards (foolproof, high performance, standards compliant, secure...),

Or maybe they were exaggerating for emphasis, as humans do.