They shouldn't be accepting either; the conditional tense is entirely separate and doesn't communicate the same thing.
This critique shows up on other future perfect exercises. The tense may be strange in English sentences without context, but that doesn't change its meaning. "Could" would require "potrebbe" in the Italian sentence. "Could have" would be "avrebbe potuto."
According to a native speaker, the following translation is perfect:
"I wonder why she left her husband!"
... and the following translation is almost as good:
"Why would she have left her husband?!"
Edit: As of November 24, 2018, "Why might she have left her husband" is accepted.
For anyone still confused about this in English: Imagine the following dialogue.
A: Next year they're getting divorced. B: No, by the end of this year she will have left him. A: Why will she have left him?
Perfectly good English.
If instead B said "...she will leave him", it would talk about her act of leaving (in the future) and not necessarily the fact that her act of leaving will be completed in the future.
The future has not happened yet, and it talks about a specific thing in the future being completed already which is why it is confusing. Compound that with the fact that this sentence structure is not very common in English, and you get native speakers saying it is nonsense when actually they would have unknowingly used similar constructions in the past.
"Partire" literally means "to depart". So it only makes sense if you're literally talking about the person leaving the room/house/location. "Lasciare" is "to leave (something somewhere)". In this specific context, it's used figuratively to indicate splitting up/divorce.
Actually I have appreciated your translation of this sentence it makes more sense than the translation provided please continue to post and to report. This is the section where I have been having trouble with the Italian and the English (I am an English speaker but the English used in translating seems as foreign as the Italian).
I really am developing an intense dislike for the future perfect tense. IMHO, I don' t think it's used very often in English, as it sounds so stilted; and, let's face it -----downright weird. Do Italians really use it all that much or is this chapter here because we are supposed to become familiar with the verb tense?
What jgierbo said is correct, but to be fair, it's because the future perfect in Italian can also be translated as the conjectural tense in English. So think of all the times you would say "must have" or "can have", and you'll probably find that it's similar to the rates at which this tense is used in Italian.
What about 'would have'? I've seen some comments in this section about conditional future, but I can't work out whether or not 'would have' is an acceptable translation (along the lines of 'must have'). I put "Why would she have left her husband" because it seemed like a reasonable way to ask the question, and far more likely to be used, but it's wrong, apparently.
When using possessive adjectives, you need the definite article EXCEPT for singular family members, where it is omitted ( * ): hence not "il suo marito" but just "suo marito". (You do need it for plural family members though: "i miei figli, i miei genitori etc)
( * ) except where the possessive adjective is loro, which always requires a definite article for family members even in the singular
But here there is no possessive adjective. It is implicit. (It is unlikely she would have left anybody else's husband, so it does not need to say that it is her husband explicitly). So the rule about omitting the definite article before possessive adjectives is not relevant here. But furthermore it is not just any old husband being referred to, but a particular one. So it needs a definite article.
I suppose it would not be wrong (perhaps just inelegant) to say "suo marito" instead of "il marito" here. What would be wrong would be to say "il suo marito".
Perhaps the most natural rendering is actually "How can she have left her husband?" This expresses the sense of the Italian pretty much exactly. Note that it does not mean "In what way was she able to have left her husband?" as a literal reading might suggest; it asks (expressing an element of surprise) how it came about that she has left her husband.
I also like "Why would she have left her husband?", for the same reason.
The future perfect tense is used in Italian not only to express what in English is expressed by that tense (here, literally: "why will she have left?", which sounds very odd) but also as what is called the conjectural future, which despite the name expresses a likely but uncertain conjecture about the past. If the sentence were indicative eg lei avrà lasciato il marito it would be best rendered in English something like "she must have left her husband". But in the interrogative mood as here, where the conjecture is not suggested but rather is being requested, it is probably best captured by eg "why would she have left her husband?" or maybe even "how could she have left her husband?" (as long as the "how?" is understood as asking for a reason rather than a modus operandi)
But in English the "-ould" does not always mean conditional-- it is the past tense for can and will also. In the context of these sentences the meaning is very much the same or darn close. Why did you do that? Why would you do that? Mean basically the same in conversational English. Why will she have left her husband means Why did she do it...or why would she do it, so Why would she have left her husband, or even why MUST she have left him, all make sense (or he left his husband, etc... no pronoun indication is given and same sex marriage exists)
But "would have" is unambiguously the conditional perfect and is not a substitute for "will have" in either language. Don't confuse similar meanings for interchangeable sentences. "Why did you do that?" and "Why would you do that?" imply different points in time and carry different implications about whether "that" was already done or is being planned out.
I take it that pablosch61 is pointing out that "would" is not solely used to express the conditional tense in English, and that just as it can sometimes be used to express the past imperfect, so also it is appropriate to use it here to express the conjectural sense which in Italian is indicated using the future perfect. That strikes me as a sound argument.
Hence "Why would she have left her husband?" is a perfectly decent rendering of the Italian into English. There is not even an implicit condition attached to this question, and that is alright: not every use of "would" requires one. Not every use of "would" is conditional.
"She would have left..." is certainly "[Lei] avrebbe lasciato..." in cases where this clause is the consequent of a conditional, but here that is not the case: instead we have the special use of the Italian Future Perfect to express conjecture. In English this task is also performed by "would have".
You can (just about) also use "will" for this, but "Why would she have left?" sounds much better in English than "Why will she have left?", and the meanings in this conjectural usage are barely distinguishable. Indeed if asked what "Why will she have left?" means, I could only reply by saying that it means "Why would she have left?" or "Why might she have left?" (though the latter question could validly be answered by suggesting some pretty unlikely scenarios which would certainly not be part of a valid answer to "why would she have left?"; so the "might" option is surely not quite right here)
I think most native English speakers understand that other languages function differently; it's just that the bizarre English translations, which often lack sense to us, make it difficult to understand what is actually meant by the Italian sentence. And that is, after all, what we're here to learn. It would be better to translate the Italian sentences more idiomatically in ways that allow us to understand the acutal meaning, rather than using word-for-word translations that lack sense.