Most natural languages, like English French Chukchi Basque Gaelic Italian Russian Latgallian Finnish Tamil and so forth, can be reasonably well modelled by a context-free grammar, which is the sort of grammar that people write computer languages in. Parsers for these are ten-a-penny. They have to be, otherwise you couldn’t run C, Perl, PHP, Python, Haskell or whatever. So a question you might be asking is why people don’t use these parsers for natural languages and go off and invent grammatical frameworks like HPSG LFG CCG and so on.
One important reason is agreement, by which I mean that verbs in English, say, agree for number and in a limited way for person. What does this mean in practice? Well, if you’re writing a context-free grammar to handle sentences like “The lady vanishes”, then you can’t just say:
S → NP VP
because that overgenerates. That would allow “The lady vanish”, “The ladies vanishes”, “I vanishes” and so on, because each of these have the form NP VP. “The lady” is an NP (noun phrase), as is “The ladies” and “I”. The rest of these sentences are all VPs (verb phrases). So our grammar has to also say:
S → NP_3rdsg VP_3rdsg
S → NP_non3rdsg VP_non3rdsg
and the same applies to every rule you have in the grammar. Modern grammatical frameworks use feature structures to look after all of this, and enable you to insist that whatever features, like number (singular, plural, and in Slovene dual) or person (I, you, he/she) words have have to agree, so you can write rules like this:
S → NP VP
and let the lexicon, the collection of the words themselves, handle the details.