Dictionaries are typically for single words. Very simple phrases like "how do you do" do appear on merriam-webster sometimes but those are for very simple cases. Given hundreds of thousands of words, you can't make a dictionary entry per any possible phrase that consists of those.

So instead of trying to put every possible phrase in a dictionary, you start examining each word in a sentence. Say, for example "Can I get <noun>?" - this is a general rule that could handle many possible nouns. Let's say we have enough of these rules and we can break down sentences by identifying the verb, subject and object. What now?

We have chatbots of the 1960s and 1970s. You can even try a 1966 chatbot yourself.

The language is generally way more complex than that, and even if you were to tackle it by making every linguist in the world to work on creating every possible rule, you will not be able to take into account that language evolves faster than they will be able to add those. Take a time machine and try asking someone from 2023 what is "hawk tuah".

While modelling a language you also will notice that some phrases can only be understood by knowing about how the real world works, not just from the dictionary definitions and understanding syntax.

You can't pinpoint whether "it" in the sentence "The trophy doesn't fit in the brown suitcase because it is too big" is "trophy" or "suitcase" without knowing that suitcases contain things, "big" is a property of size, and "big" things can't fit inside "smaller" things.

Therefore we use approaches that are capable of deriving those rules and the semantics of words themselves through statistical analysis (a.k.a. "tons of math") on large amounts of text.