Reading down the comments at CT it sounds like she had been taught a “right” answer to why it is true in general, though. Something like: “You have an even number of things if you can put them pairs and an odd number if there is one left when you try put them pairs. If you add odd to odd you can pair the the two ‘spare’ ones (and leave the rest paired as before)”.

On the one hand having an early familiarity with this sort of general argument seems like a Good Thing but on the other I’m not sure how useful it is to just have them parrot back “the spare ones pair off” (all they could hope for in that space).

I can’t see how one could expect a small child to answer any better, but whatever the kid writes, at least (s)he has been encouraged to think about the question. I’d guess that a lot of kids work out the answer in their heads but then can’t articulate it, especially given such a small space to write their response.

(I had a Pushy Maths Dad who was always asking me this kind of thing when I was a littl’un. I think it helped.)