It is only when Portia gives a sign of her own 'manliness' (which in this play is equated with 'Romanness'), that Brutus gives in and promises to share with her the secrets that he has already yielded to his male friends. Interestingly, the sign that Portia gives of being a manly Roman woman, able to keep secrets, is a voluntary wound to the thigh (2.1.301-2). This is a sign of her Stoic self-control. But it is also an act of self-penetration: like a man, she wields the sword, but suffers for it as a wounded woman.
Roman manliness is in fact associated with health. Immediately after the scene in which Portia reveals her wound, Brutus receives his sick friend, Caius Ligarius, speaking with "feeble tongue" and with a "kerchief" on his head. But when he joins the conspiracy to restore manly republican virtues to Rome, he throws off his sickness. Julius Caesar, with his epilepsy, his deafness, and his barren wife, symbolizes the weakness and effeminacy that sets in when those republican virtues are abandoned. (Cassius' mean-spirited story of his sickness on campaign, crying for something to drink "as a sick girl" is intended to make this same point.)
Thus, Republican Rome can only be governed by men, and can only admire women who are like men. It's opposite, called 'tyranny', is associated with feminizing degradation, as when Cassius exhorts Brutus with this passage of inflaming metonymies:
... our fathers' minds are dead,
And we are governed with our mothers' spirits
Our yoke and sufferance show us womanish ....
(1.3.82-84)