It depends on the precise wording. If anyone is being taught that gender is a free choice then they are being taught incorrectly -- the entire point is that it's not a choice but an innate part of who you are. On occasion, the sense of self and the biological are misaligned, but even in that circumstance it's no choice that's being made, except perhaps to no longer deny what your mind is telling you. So anyone who spreads a message to young children that "you may look like a boy/ girl but you don't have to be -- no, really, you can be whatever you want to be if you like! Honest, don't feel bad if you decide to be something different" is in the first place wrong and in the second place indeed risks pressuring someone into trying to make a choice not out of what they want but out of what they think others do. This doesn't happen often but whenever it does I'd frown on it as much as the next person.
I don't think this is actually what the Pope is complaining about, though, and he is rejecting even the concept that biological and social gender can ever be misaligned on principle. This is simply wrong, but the head of an institution bound to ancient dogma is hardly the easiest person to persuade of this. The message that gender is a choice is wrong, but the message that transgenderism is a reality of some people's lives that should be respected is certainly not damaging, whether or not it's taught to children.
It's disappointing, but hardly surprising, that the Pope (and Khandro, among others, in turn) fails to appreciate the difference between gender identity as a choice and as something that transcends biology.