While there isn't a norm on women being forbidden from leaving the house, even Ancient Sparta seemed not to have their women in the Assemblies and Councils. Why? Does it have something to do with the "Man represents the whole Oikos" or something like that? I thought the sons of a citizen also could exercise their rights even when leaving with their fathers (though maybe the age bar played a part here)
And I know Athens was highly misogynist but I don't understand how then the women can be citizens as much as men and yet being barred from political power, other than priestesses.
Who told you women were full citizen? They weren't, plain and simple. They didn't exercise any rights in the democratic bodies because they didn't have such rights.
See for example Thorley (1996): Athenian Democracy, p.74:
The fact remains, however, that women did not have any political rights in the Athenian democracy, and scarcely any legal rights either; in law they were always regarded as being under the guardianship of a male member of the family.