brain sex can sell lots of copies of cosmo, and create lots of clickbait on buzzfeed, as it upholds the conservative ideal of gender binaries. but, if you ask an actual scientist, that person will tell you that it's not actually really a thing.
our brains are not planned out by god, or by dna, or by aliens, or by any other mystical force. they are constantly changing organs. this ability of our brains to morph and change - rather than develop due to a set plan - is called plasticity.
what it means is that we are literally the products of our experiences. tabula rasa, baby! our brains can and will and must and do change depending on the environment that they exist within.
when you begin to understand the brain as this constantly shifting ball of plasma, rather than as this fixed identity given to you by god, the idea of a "brain sex" stops even being coherent. how can a brain have a sex if it's constantly shifting and adapting to the environment? what does that even mean?
the abstract suggests that there are sex differences, and we exist on a spectrum, but this is a poor use of language. what they should be talking about is how experiences cluster with gender roles, making it more clear that the overlaps are a consequence of experience, rather than of biology.
transgendered people do not have a genetic abnormality or a psychological disorder. we are merely a product of human variation. a truly liberal society would uphold our rights to make choices, not try and diagnose us with an illness and claim we don't have a choice and don't understand what we're doing.
but, we're coming up to the end of this fruitless search. the science on this is winding down. and, we're going to have to confront the reality that it hasn't found anything, and instead deal with the actual issue in front of us: that we are free to make these decisions and need legal structures to uphold our rights of free expression.
http://www.pnas.org/content/112/50/15468.abstract