In all sincerity, this question is almost identical to "what's the most difficult thing about building an operating system" as a modern browser is tens of millions of lines of code that can run sophisticated applications. It has a network stack, half a dozen parsers, frame construction and reflow modules, composite, render and paint components, front end UI components, an extensibility framework, and more. Each one of these must enable supporting backward compatibility for 30 year old content as well as ridiculously complex contemporary web apps. And it has to load and render sites that a completely programming illiterate fool like me wrote. It must do this all in a performant and secure way using minimal system resources. Also, it probably also must run on Mac, Windows, Linux, Android, iOS, and maybe more.