Parser generators work really well for context-free grammars, but as soon as you start needing context-sensitive lexing (like C does) you enter World Of Pain time. And they avoid having to deal with lookahead, which is always messy in hand-written parsers.

But I think I'd agree that writing a recursive descent parser from scratch is probably the best way to learn about parsing; at least for a simple grammar.

BTW, fun fact: it turns out that BNF was invented by an Indian linguist called Pāṇini about 2500 years ago, in order to parse Sanskrit.

https://en.wikipedia.org/wiki/P%C4%81%E1%B9%87ini