Microsoft word seems to think it should be "Why are x good and y bad?" and I don't agree because that doesn't sound right. And yet I can't really think of why either should be better because "y bad" is not a complete sentence in its own right. Meanwhile, writing "Why is x good and why is y bad?" seems redundant. And if I treat "x good" and "y bad" as subjects in subject verb agreement then it leads to the really awkward sounding sentence "Why are x good and y bad?".
It's an interesting example. I agree with your judgment, but it is not obvious why "be" should not agree with what appears to be a plural subject: "x good and y bad". I think the answer is that "be" does not actually have a plural subject.
[[x is good] and [y is bad]] for some reason. Why?
I've enclosed the coordinated subject in brackets. The wh-word replaces "for some reason" and goes at the beginning of the wh-question:
why [[x is good] and [y is bad]]?
As with all wh-questions, when the wh-word is not the subject, subject-auxiliary inversion applies to move a finite auxiliary, here "is", to before the subject. So we have to move "is" in front of the subject "[[x is good] and [y is bad]]".
In McCawley's paraphrase of Ross's CSC (Coordinate Structure Constraint), any change to one conjunct of a coordinate structure has to apply equally to the other conjunct, so what has to be done in this situation is that "is" has to be removed from both the conjuncts of the subject and put before the subject. After we do that, we get
Why is [[x good] and [y bad]]?
Note that in this derivation "is" never has a plural subject. That's why it doesn't change to "are".
In general, whenever there's a redundancy, you can omit the redundant words to make the sentence more elegant. That's all that's going on in your sentence. Here's another example:
I am the tallest one in my family; Jojo, the thinnest.
Sorry, that's not an exciting example, but hopefully you see what I mean.