I remember reading Plato as an undergrad and being interested in the way Socrates took pains to define his terms in the dialogs.
Western philosophy has continued this tradition, and by the 20th century, the problem of meaning in philosophical language became acute.
The problem goes like this: If you want to make logical constructions using regular language, you need both clear and consistent meanings, which, as it turns out, regular language is really bad at doing.
Meaning in language is context-specific. If you say “Stay warm out there!” when it’s 20 below, people will take it in a fairly straightforward way. If you say it when it’s 110, people will think you’re being sarcastic.
Worse is the logical purpose behind saying it at all. In the first case it’s obvious and in the second unnecessary, so saying “Stay warm out there!” must serve some other social purpose than just telling people what to do.
Defining our terms, then, can be useful in order to establish context and purpose: such as within a technical manual or a textbook—or even a political debate.
So if it seems like we’re talking past each other, maybe we should step back a bit and start again by defining our terms.