"Why do you cry?"
As the word "you" is already included in "piangi" you should not repeat it.
That is unless you want to put emphasis on you, - but then you should put it at the end of the sentence, "Perché piangi tu?"
Then, as the English word "you" has several meanings, this can also be translated as:
Perché piangi? (you = tu)
Perché piange? (you = Lei)
Perché piangete? (you = voi)
Just a little insight regarding this construction: "why do you cry?" refers to crying at any time rather than at a particular time (suggested by "why are you crying?").
As such, non-natives should be aware that it sounds quite clinical, such as something a scientist might say in his thesis to investigate why humans cry. Or similarly, an alien/robot that doesn't understand the concept of crying. :)
Apparently Duolingo, which usually doesn't acknowledge the formal you ("Lei"), did this time. So technically it's tu piangi, lui/lei/Lei piange. But since Duolingo doesn't teach the Lei form, they shouldn't have included it here. I've noticed they've done that on another question as well.
The exercise I did on 28 Aug 2017 to get to this discussion gave two answers, one using piange and the other piangete in tranlating "Why do you cry." The first time through, I didn't select piange, and was marked wrong. The second time I selected both.
What bothers me about this is that the verb forms are the formal you Lei painge and the plural you voi piangete. On more occasions than I can to count, Duo has disallowed the Lei form of verbs. Very fickle of it to require it now as a correct answer.
Do you use Windows? Are you a native US English user?
If so, you can load the US-International keyboard, replacing the default US English keyboard. At that point there are a number of ways of entering accents using the ' ` " and ^ keys before typing a letter. For example: è, é, ë, ê.
After all of the sections I've completed, this is the first time I've ever heard of the formal singular Lei! I thought Voi covered both formal singular and informal/formal plural. Frustrating! This will take quite the adjustment to get used to and I think it should have been addressed sooner.
conjugation form of a verb in 3rd singular person is in Italian also used for formal/polite addressing someone who we do not know, who deserves the respect, in Italy almost always someone who's elderly. Same with imperative forms, but there is some confusion here, as the verb's endings do differ. I'm sure you know how to say "scusi" "scusi" is a polite/formal form as in imperative this is the 3rd singular person (do not be fooled by the "i" ending, that how it goes in imperative. "scusa" on another hand is just informal way to address your friend ("a' ending is in 2nd singular person, this confuses a lot of people so before you you press "CONFIRM' button always think twice about which person it is, formal/informal form, and is it imperative? to avoid common mistakes) if you are not sure, use this: https://www.wordreference.com/conj/ItVerbs.aspx?v=scusare
Good question. So it is not, just it is not. Take it as it is. That's it. But as every language is different in some languages "to cry" can be both (reflexive and not) so you could for example "cry yourself to death". But as I see not in Italian. if you have any doubts, you can always check any verb here: https://www.wordreference.com/iten/piangere
"piangi" is correct as you already know.
"Perché piange?" means "Why does he/she cry?". So it would be a very correct (grammatically) sentence, just not the right translation in this case.
DL does not have to give us all ready to use forms of the verbs on the plate, and they do not. We have often to look stuff up in a dictionary.