If this has been your experience, I'd encourage you to consider why that might be the case.
Here's one possibility: Perhaps in our culture, assertive women are treated worse than assertive men.
You can see this dynamic in the dating world where non-assertive men are the losers of the game.
It can explain average population outcomes like men on average haggling for better wages as you said.
It can also explain outlier outcome, for example the most disagreeable people are mostly men. This makes men more likely to end up in prison. Which doesn't mean that the average men is much more likely to end up in prison than the average woman. But the type of person who is more likely to end up in prison happen to be mostly men.
[1] https://en.wikipedia.org/wiki/Agreeableness [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3149680/
That's a descriptive, not necessarily a normative, statement. What's more interesting to me is why women and men act differently. Do you believe the differences could be the result of child rearing, social climate and norms etc?
IF being more assertive is proven to be a naturally masculine trait, then shouldn't discriminating against men for a natural behavior be seen as sexism as well?
The question is ill-defined, those terms, sexism and natural ..., don't have to be mutually exclusive. Thew comparison doesn't even make much sense, see also https://en.wikipedia.org/wiki/Appeal_to_nature
Your implication is paradox, because it paints with a pretty broad brush and out of line. You suggest that discriminating against naturally gender specific behavior is sexism. I don't think that's the case, although it's a loosely defined, broad term. At least sexism is a stereotype, too, yes.
Paradoxically, women who are discriminating against men would be assertive. Therefore you would be in turn discriminating against this presumably unnatural tendency (unless women aren't vocal about this). That's ironic because as far as I know sexism fundamentally is against ascribing any character attributes based on gender, analog to racism. (I might be confused here, because it's not usually my debate. Popular sexism is rather against discrimination in face of obvious gender based properties, like pregnancy.)
On the other hand, casual sexism is just the exercise of sexism, whether it be natural or not, in settings where it doesn't belong. In general, professionalism requires an extend of discretion and privacy and is certainly not black and white at that, but rather subjective. And that's what emancipation is about, incidentally, to be treated as a subject, individually, and not objective as a stereotype.
The issue I see is that a lot of these issues are just about being in "a minority group". But a lot of complaints are levelled against the "male gender". This is sexist. Everything else is not.
Sexism has to be when people are treated differently solely because of their sex. In the tech world and corporate world, there is often a large imbalance between male and female, so that the treatment of a minority group appears sexist, because females are usually the minority.
The best test is to reverse the groupings and apply the same test.
When you think about it like this, it becomes less about "men" being somehow inherently bad which is a gross generalisation, and more about "humans are terrible people sometimes". But the issue with the latter statement is its not easy where to throw the blame.
Its just one data point, but it correlates
So if a person is speaking over you and rambling on, perhaps a man is more likely to speak up or butt in at the first opportunity. The quote in the top comment sort of hints at this. That she didn't feel as annoyed by his talking and so didn't speak up. I haven't watched the whole thing, but other comments mention he does this over male panelists as well.