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if you start with just 11 books, spines all matched on one side. you have 11 non spines on the other side.
You can then add 11 books facing the other way under each of the original 11, plus 1,also facing the other way, on top... surely. or am i missing something in the clue?

oops then you would count 12 spines - non spines on each side,
my apolgies, ?I'll sick to the crosswords.

Well, the 'maximum number' wording is a bit confusing. I don't see how there can be any more or less than 21 but who knows?

After pondering this and remembering that at School I learnt that 11 telegraph poles are needed to suspend 10 lengths of telegraph wire, I decided to follow Mamya's suggestion.
The pile was not neat. I ought to have chosen smaller books more similar in dimensions. The pile was unstable -but I had 22 books

Strongly suggest you check again.

agreed

OK - it's definitely 23!

Doesn't it depend on where you start counting? If the first book in your pile/row is set spine facing and you count that side as non-spines you will end up with one book more than if you count that side as spine-facing. So, 21 or 22 depending on where you start, maximum 22. But I don't see how you arrive at 23.

23 would give you 12 spines on one side which goes against the question. 22 seems to be the maximum.

How is this a crossword??