The formal patterns of correct reasoning can all be conveyed through ordinary language, but then so can a lot of other things. In fact, we use language in many different ways, some of which are irrelevant to any attempt to provide reasons for what we believe. It is helpful to identify at least three distinct uses of language:

The informative use of language involves an effort to communicate some content. When I tell a child, "The fifth of May is Mexican Independence Day," or write to you that "Logic is the study of correct reasoning," or jot a note to myself, "Jennifer—555-3769," I am using language informatively. This kind of use presumes that the content of what is being communicated is actually true, so it will be our central focus in the study of logic.
An expressive use of language, on the other hand, intends only to vent some feeling, or perhaps to evoke some feeling from other people. When I say, "Friday afternoons are dreary," or yell "Ouch!" I am using language expressively. Although such uses don't convey any information, they do serve an important function in everyday life, since how we feel sometimes matters as much as—or more than—what we hold to be true.
Finally, directive uses of language aim to cause or to prevent some overt action by a human agent. When I say "Shut the door," or write "Read the textbook," or memo myself, "Don't rely so heavily on the passive voice," I am using language directively. The point in each of these cases is to make someone perform (or forswear) a particular action. This is a significant linguistic function, too, but like the expressive use, it doesn't always relate logically to the truth of our beliefs.
Notice that the intended use in a particular instance often depends more on the specific context and tone of voice than it does on the grammatical form or vocabulary of what is said. The simple declarative sentence, "I'm hungry," for example, could be used to report on a physiological condition, or to express a feeling, or implicitly to request that someone feed me. In fact, uses of two or more varieties may be mixed together in a single utterance; "Stop that," for example, usually involves both expressive and directive functions jointly. In many cases, however, it is possible to identify a single use of language that is probably intended to be the primary function of a particular linguistic unit.

British philosopher J. L. Austin developed a similar, though much more detailed and sophisticated, nomenclature for the variety of actions we commonly perform in employing ordinary language. You're welcome to examine his theory of speech acts in association with the discussion in your textbook. While the specifics may vary, some portion of the point remains the same: since we do in fact employ language for many distinct purposes, we can minimize confusion by keeping in mind what we're up to on any particular occasion.