«о́бувь» is more like "footwear". It is already a singular mass noun and does not really have to distinguish between one and many.
If you mean a non-sports shoe, reaching maybe your ankle but no higher, it is usually ту́фля (a dress shoe, or a woman's shoe) or боти́нок (preferred by males to describe their shoes, though, more in spoken speech). High "boots" are сапоги́ (singular «сапо́г»).
And, of course, sneakers and flip-flops are their own thing. If you need an umbrella term, it is still "footwear" (обувь).
I think, as can be inferred above, because the semantics of "моя обувь" would be equivalent to "my shoes" in English. Like you don't say "my pant" or "my trouser" even though they can be technically correct but it would have been an odd case. I got this wrong too, but after seeing these explanations I'm more inclined to accept it's better marked the answer "my shoe" incorrect. And I WAS wrong to assume singular, even though it could be argued I don't have to be wrong.
preferred by males to describe their shoes
Not in Belarus, I guess..? I've only seen «ботинки» written on tags in shops, but never heard anyone use that word, only «туфли». I'm pretty surprised to hear it's 'preferred'.