Maybe it's because I'm not an English native speaker, but I don't understand why "The big Klingon sees himself" is wrong. Someone could explain me?
"Big" in English refers to something that's large in mass or in volume. It may be tall, or it may be wide, or it may be large in all directions. Sometimes we use "big" to refer to someone's height, but we are applying it in a general sense. Klingon has a word with very similar meanings and uses - tIn.
"Tall" specifically refers to height and is relative, but implies more height than expected. It is a more specific word and rarely, when "big" is being used to specifically refer to height, the two words can be used interchangeably. Klingon also has a word with very similar meanings and uses - woch.
While it is possible for a person to use the word "big" when they mean something is "tall", this course teaches these words as being different and meaning different things, just as the English words do. Thus when you see the word woch, you should translate it as "tall" and when you see the word tIn, you should translate it as "big".
The obvious answer: because it's not one of the accepted alternatives that had been entered manually as possible translations of the sentence. Most of the exercises don't accept "singular they" because that alternative hadn't been added - for whatever reason.
We've talked about whether to include it in the future.
However, apart from the effort of revising thousands of sentences to include "singular they" in all cases where "he" and "she" are both accepted, one reason not to include it is that we want to make sure that learners use the Klingon prefixes accurately. It's hard enough that "you" in English is both singular and plural you; if we included both singular and plural "they" as well, it would be difficult to recognise which translation into Klingon is expected, or whether a translation from Klingon was correctly understood or not.
wIlegh, for example, can only have a singular object -- we saw him, we saw her, we saw it. If we accepted "we saw them" as well with singular they, a learner might think that wI- works like vI-, Da-, bo- (I ..., you ...) which are the same whether the object is singular or plural. But "we saw them" (with plural they) has to be DIlegh. And so on.
One possibility would be to accept singular they for sentences where the remainder of the English definitely makes it singular, like here. But that would also be a bit inconsistent, and there might be corner cases where it's not quite clear whether singular they would be unambiguous enough or not. Plus again there's the effort spent on going over thousands of sentences and deciding which ones quality, then working on them -- time that could probably be spent more productively making more pressing changes. (We're just three of us, working on this in our spare time, of which there is never enough.)
Klingon is grammatically gender neutral -- the Klingon is looking at ghaHself, which could be himself, herself, or (singular) themself. Even zirself or emself, if that's what you would say in English.
But for the purposes of this course, I recommend that you go with either "himself" or "herself".