So there were some texts later discussing the problems of Elizabeth I being Queen Regnant when all laws and customs referred to a “King.” We also see a lot of her father’s behaviour (Henry VIII) being driven by his need for a male heir. It’s why he tries to annul his marriage to Catherine of Aragon.
Further, there were specific reasons why Elizabeth I was treated differently to her father. For example, Henry VIII used to meet with counsellors when he woke up in the morning, still in bed. For obvious reasons, this was not done when his daughter reigned.
I don't think that's why it's called a "Privy Council". Just because the only meaning for privy that you know, today, is a toilet, does not mean that the word in another context means toilet, any more than the fact you know the verb "do" in English can be slang for sexual intercourse means that when Marlo says "Do it or don't" in The Wire he means for his soldiers to have sex. He's indicating that he doesn't care whether they murder Bubbles.
"Privy" more generally means private or personal, which explains its use for a group which advises specifically the monarch alone.
> According to the Oxford dictionary the definition of the word "privy" in Privy Council is an obsolete one meaning "Of or pertaining exclusively to a particular person or persons; one's own",[3] insofar as the council is personal to the sovereign.
