The most usual way to make a future tense is with θα. Θα comes from θέλω ίνα, I am going to that transformed to θέ νά and finally θα. Since θέλω means I want, it is not so different this itinerary from the English furure as will comes from the same verb. There are other ways to express future in Greek, as πρόκειται να, I am going to. The present tense can be used too with the meaning of future, or past tense, depending on the context or a time adverb, i.e. έρχομαι (στην) Αθήνα αύριο, I will go to Athens tomorrow.
Except that doesn't Greek often use the progressive when in English we don't? That would be why the future form is used in English, not the future progressive. We want to translate so that the meaning is the same, not translate word for word and end up not actually understanding what we're saying. (I say this except for idioms - I hate when Duo translates one idiom to another so that you have no idea what the original even says...)
While I understand the distinction in use between the two Greek forms -- without context, I still think εσύ θα πίνεις could nevertheless be translated as "you will drink," if we added something like "... every day for the rest of your life." As others have said, trying to enforce the distinction between the two futures in a "Basic Phrases" lesson should be a pedagogical no-no.