Or is it some kind of English grammatical transgender?
Basically... yes, exactly. Linguistically, it's referred to as a "semivowel", since it represents other, non-vocalic, sounds as well as vocalic ones. But since offhand I can't think of a single word in any language that uses the Roman alphabet where a final-y has anything
but a vowel sound (or at least is part of a vowel diphthong), calling a final-y a "non-vowel" is
really nitpicky even by my standards -- and I'll readily admit that I can be seriously-annoyingly-nitpicky where language is concerned.
As for the OP, honestly, it
is pretty lame. I'd have some sympathy if she'd said "France", for example, which doesn't end in a "vowel sound" even though it does "end in a vowel". But since I imagine that at least half of all British toddlers have been thoroughly exposed to the concept that "Paris" is a "city", and the English-language names of pretty much
every country
anywhere near the UK
except France end in consonants (assuming you consider "y" a consonant for this purpose), it's really kind of sad, however understandable brain-freeze might be in general... I mean, you have to go all the way to
Austria to find the first one that has a "vowel sound" as well as an actual vowel at the end of its name, for heaven's sake, leaving a true multitude of possible
correct answers - from Swede
n to the north, to Spai
n to the south, Irelan
d to the west, and most everything to the east until you get all the way to freaking Austria (except of course France, where Paris is...), for God's sake...