We have empirical evidence that simple speech can involuntarily lower math exam scores in women.
We do? Citation, please. Bear in mind that positive or negative feedback can affect behavior to a certain extent in both men and women; that's why we encourage kids. I wouldn't be surprised to see evidence that encouragement or discouragement affects behavior. I would be surprised to see evidence that the effect is greatly amplified in women.
Banaji et al. have a substantial body of work on the topic. For a good overview I suggest
this Wikipedia page. This page, however, is hardly up to date; it fails to note how extremely subtle the triggering stimuli may be, and the fact that they can be presented as subconscious primes (a female face blinked for 4 milliseconds, below the threshold of conscious detection, for instance.)
I admit to being mildly peeved that you think this has something to do with positive or negative encouragement. Research psychology is hard science. There is very good, very well-controlled research happening here, and it is well beyond the level of simple encouragement. Encouragement is a System 1 conscious process; the process we look at here is not resident in consciousness.
This is the topic I perform research on.
The mechanism of stereotype threat means that a misogynistic individual can actually force women to conform to stereotypes simply by subconsciously activating those stereotypes.
If this is true, it means that women are a lot more psychologically fragile than I have historically given them credit for. Does a simple verbal taunt affect their constitution to that degree?
Are iamzack and Rian etc. psychologically at risk by reading High Max's posts in thread?
Maybe you should clarify what you mean here. Because that statement certainly sounds like it could be used to prove High Max's case. 
It has nothing to do with being a woman. Indeed, it has nothing to do with
any conscious factors, including emotional stability. The effect is entirely resident in System II automatic processes which occur far outside of the spotlight of awareness and without significant detection or interference by System I consciousness.
The effect can be induced in white men, black men, white women, black women, Asian men, Asian women - anyone. All that's required is a relevant stereotype. (The issue is, of course, that there are far more harmful stereotypes about women
vis a vis men...though it is not purely in the man's favor.)
Ask white men to identify their race before playing basketball? They perform poorly compared to a control group. White men can't jump.
Ask Asian women to identify their race before a math exam? They do well at math. Asians are good at math.
Ask Asian women to identify their gender before a math exam? They do poorly. Women are poor at math.
Ask Black individuals to identify their race before taking a simple GRE test? They get about half as many questions right as a control group. Black people are stupid.
These are all controlled experiments, mind. The only difference between the experimental group and the control group is that the experimental group ticked a little box or read a little essay or heard an off-hand remark.
The stereotype activation is unconscious; it is not anything they are aware of. Staggeringly, I can have you
read an article about old people, and when you stand up and walk away, you will
walk more slowly than a control group. It has nothing to do with encouragement or discouragement.
Simply ticking a box to identify race or sex will do it. Hell,
reading an article will do it.
Isn't that nuts?
You can force people to act in accordance with stereotypes. Even if they don't want to. Even if they dislike the stereotype with all their hearts. A woman could rant at you about how men are only capable of feeling anger, and, believe it or not, you would probably be primed to exhibit greater anger. It's not something that only works on women, it works on
everybody. But the problem is that the stereotypes associated with women are more broadly negative (and, yeah, I'll cite that too if I can find the papers.)
EDIT: And here's an example of the kind of conundrum women have to face all the time:
"Thus the predicament of 'stereotype vulnerability': The group members then know that anything about them or anything they do that fits the stereotype can be taken as confirming it as self-characteristic, in the eyes of others, and perhaps even in their own eyes. This vulnerability amounts to a jeopardy of double devaluation: once for whatever bad thing the stereotype-fitting behavior or feature would say about anyone, and again for its confirmation of the bad things alleged in the stereotype."
A woman going into a math exam not only has to deal (subconsciously!) with the knowledge that 'women are bad at math', but also (consciously or not) with the knowledge that if she does poorly at math, it will confirm opinions that women are bad at math! Talk about double jeopardy.
And this is why it's so important that women be allowed to speak up - because it would be tremendously easy to say 'women are *****es, they complain.' It's already part of the female stereotype. It's a powerful and effective way to dismiss the voices of women.
tl;dr version: the cognitive loophole that creates this vulnerability is present in everyone, not just in women. But it harms women and racial minorities far more often because they have so many more negative stereotypes associated with them.
A great example: you can run an experiment where you have a subject perform a really boring number-identification task for two hours. Between each set of numbers, a face is flashed for 3 or 4 milliseconds, faster than the conscious mind can adapt. The face is either Black or White. The subject is totally unaware of these subliminal flashes.
After two hours, the computer crashes, and an experimenter tells the subject that they will have to do the study over again. The participant's reaction is videotaped, and the amount of aggression and anger coded by a blind panel.
Subjects who saw Black faces exhibit far more aggression than those who were primed with White faces. They have no idea why. They have no idea they were seeing faces. At no point did this even enter their awareness.This stuff is both fascinating and kind of terrifying. And, ironically, people are far less receptive to it than the idea that everyone carries their own personal clock and that time is not universal (see relativity.) Nobody likes to hear that their own brain has bugs in need of patching.