Consider the following valid argument:
Given: If Tom goes to the hardware store today, he will buy a hammer.
Given: If Tom buys a hammer, he will have change for $10.
Conclusion: If Tom goes to the hardware store today, he will have change for a $10.
On the surface, your argument seems identical to the above. However, once you say "most" or "in general", you are making a statistical statement. Let's state and validate your statement using statistics:
Given: If we randomly select a man and a woman, and give them a completely accurate assertiveness test, there is a probability p (greater than 50%) that the man will score higher and thus be deemed more assertive.
Given: If we randomly select two people (without regard to gender), and send them randomly to two salary negotiations, the more assertive person has probability q (greater than 50%) of receiving a higher offer.
Note that, if we randomize sufficiently, the only thing that must be perfect is the assertiveness test. All other factors should cancel out. We are also either assuming that past performance implies future performance, or that the givens above are somehow known to be absolutely true.
We now statistically establish your conclusion by looking at the 4 cases:
The man is more aggressive (probability p) and the more aggressive person receives the higher offer (probability q). Total probability: pq (we can assume independence because we are using random selection).
The man is more aggressive (probability p) but the less aggressive person gets the higher offer (probability 1-q). Total probability: p(1-q).
The woman is more aggressive (probability 1-p) and the more aggressive person receives the higher offer (probability q). Total probability: (1-p)q.
The woman is more aggressive (probability 1-p) but the less aggressive person receives the higher offer (probability 1-q). Total probability: (1-p)(1-q)
The man receives the job in cases 1 and 4, for a total probability of pq+(1-p)(1-q). Since we assume both and p and q were greater than 50%, pq+(1-p)(1-q) must also be greater than 50%
Therefore, even at a statistical level, your premise is valid: if a randomly selected man and a randomly selected woman enter a randomly selected salary negotiation, the man is more likely to receive a higher offer than the woman.
Now, let's walk into a trap.
You see two people who will be interviewing for a job. One is a woman, one is a man. Probabilisticly, who is likely to receive the higher salary offer (assume that the offers won't be identical-- failure to get the job is an offer of $0).
The obvious answer is "the man", but this is incorrect because I left out the key phrase "randomly selected".
Looking at the pair, you may notice they have different heights, weights, ages, are dressed differently, and so on. More importantly, there are plenty of differences you can't notice: how many years of education they have, what their work experience is, even what they had for breakfast, whether they were born before or after noon, etc.
If there are 500 people in town, there are 2^499 different ways to separate the pair into two groups, and, statistically speaking, each grouping is equally valid.
"But I only have data on gender", you may say. True, but this means you introduced a bias when you chose to look at gender instead of the 2^499-1 other ways of separating people. You decided gender was something important to look at, even though there are necessarily more important factors (or "combinations of factors", which are still technically factors), even if they don't have simple names in our language.
This is why some people believe governments shouldn't release data on a criminal's race, for example (some countries already don't do this). By listing some characteristics of criminals, but not all of them, there is an implication these characteristics are more important than other characteristics. If you could somehow list all characteristics, you would find some characteristics have an ever high correlation with criminals.
As a silly example, you might find that men who are currently over 5 foot 7 inches tall who were born in Kentucky but moved to Indiana between the ages of 7-9 and then subsequently moved to California for at least 2 years sometime in their lives, are registered Republican, and chose Ginger over MaryAnn in a survey, have a crime rate 100 times higher than average.
It's unlikely we would regard people with those characteristics (who haven't already committed crimes) as dangerous. We would attribute it to random chance, but statistically, that characteristic would be just as valid as race or other factors some people actually to attribute to criminal risk.
