You can't parse fully-general HTML with regex, but unless you're writing a web browser of something, that's not what you're trying to do; you're trying to parse

You can't parse fully-general HTML with regex, but unless you're writing a web browser of something, that's not what you're trying to do; you're trying to parse the particular subset of HTML that happens to be emitted by this particular website that you got the HTML to be parsed from. And, much like the halting problem or integer factorization, despite the general case being difficult or impossible, the overwhelming majority of specific cases are easy.