"I drink tea every night."
毎晩 appears to be the set phrase. I'm sure you could say まいよる or まいゆうべ and be understood, but if you look up "every night" in a dictionary like jisho.org, 毎晩 is what comes up. The way I think of it is like this -- if you were learning English, you might think that "evening" and "dusk" and "twilight" all have similar meanings, the time when the sun is going down but it's not yet full night, and yet nobody says "good dusk," only "good evening." Some phrases are just set.
Just because it's on Jisho (or in any other dictionary for that matter) doesn't mean it's commonly used. There are words on the internet that you can't find anywhere apart from their dictionary definitions. As has been said, you could end up saying things like “good dusk”.
You can instead have a comma, making it a separate part of the sentence that sets the scene, rather than the subject of the sentence. The equivalent of doing this in English: "Every night, I drink tea" Whereas using は after 毎晩 integrates the "every night" into the full sentence, and might sound a bit more like: "I drink tea every night" (and also carries more emphasis on the "every night"). I believe Duolingo usually accepts both answers though.