If that's vitriol to you, you need to read the Philippics my friend. That is ancient vitriol.
Firstly, I'd like to make it clear that you do not have to hate someone in order to oppress or suppress them; you simply have to view them as 'other'.
And that was the Greek view of women - other. Bri's use of 'essentially like children' was to explain to you the concept of how they were othered without active hatred... because do you think they hated their male citizen children??
Do you really think they hated their future male citizens??
Of course not, but they're in the same box because they've been 'othered' as "not as rational as men".... that doesn't mean hatred, and that doesn't mean vitriol. It means 'other' and 'different' and 'not suited to X, Y, Z task'.
This, then, translates into the treatment of women.
If in Athens women are viewed as less suited to certain tasks due to this belief over rationality - namely, the task of statesmanship...which was the key job of the elite Athenians (bear in mind it's only really them we have a full record of 'this is how women should be suppressed' from... and even that's a 'they should be' not a 'they are') serving in a Democracy, then yes, they're going to be seen as lesser because they can't serve the state in the same integral and public way as men could.
Thus, if you can't serve the state to the same capability as these men, you get put under their 'protection' (i.e. your rights are inherently linked to theirs... which is how women were treated like children in Athens)
Now, that's all just Athens... but you see how that isn't full of vitriol and hatred, it's literally just based on "women are different than men, namely in their rationality and physical strength, thus they can't serve in wars (the elite classes were also the main heavy-armed troops - hoplites; we're talking like 30kg of armour - it's HEAVY) and can't serve in politics... thus they don't serve the state publicly and must be put under protection of those who can."
I happen to specialise in Sparta, where women took an active part in athletics publicly, where they were well educated and took a key role in their sons' educations; certainly a place they weren't "hated" - but again they weren't in government... because the Spartan government was made up of the warrior classes yet again, and frankly the women were too busy running everything else to be able to train and serve too!
Just to parrot your own phrasing....
"Minimising the multitudinous and important roles of women in antiquity to just 'they were hated on' because you're misinformed about it, isn't the take you think it is."
It's actually quite a dismissive one.
The treatment of women in antiquity is inherently linked to the formation of the state, and with that, the military history of the state and the associated practicalities. They were not hated, they were treated as 'other' based on those grounds. That does not mean we have to approve of how they were treated, or that we agree it was right... it simply means that their treatment was not because of hatred.