There are other papers showing the same sort of pattern elsewhere. For example, you can see one cited in that paper within the introductory paragraphs.

As the commenter upthread noted, the adult demographic is more weighted towards men who want to be women. Why would childhood referrals have become shifted in the opposite direction, much more towards girls who want to be boys?

Why is the question;

> There's not really any plausible explanation as to [..] other than social contagion.

is a leap.

> Why would childhood referrals have become shifted

\1 Have they really shifted, or have the stats on a relatively new thing in a few countries firmed up from nothing, to bugger all, to enough to see a pattern?

\2 As to the pattern now seen - a few boys question whether they like being boys at an earlier age than a few more girls then question whether they like being girls ..

there are other factors, eg: I heard there's a "big change" in the lives of young girls at an age that coincides with a 'surge' (small numbers in a country the size of the UK) in girls exploring whether they want to be girls after all.

Social patterns, depth of communication about places existing where gender question can be asked, word of mouth, etc are factors that play a role - but they are not the sole factors at play in these very low incident observations.

My suggestion to yourself, looking at the questions you've raised and how you've framed them, is to perhaps study some epidemiology and find a mentor with first hand real world experience with low frequency data that gradually comes to light as social norms about reporting evolve - eg: SIDS data in the 1970s / 1980s.

You seem to be making a great many mistakes based on preconceptions and "feels".

If only the Dutch hadn't destroyed quite so many records in "their" East Indies .. there might be other gender frequency records to draw on <shrug>.