I am not a history guy. But, from what I have collected from movies, TV shows and people, I see that old British society was male-dominant and there were female rights issues too. But, I also see some powerful queens in the history and the "for Queen and the Country" thing. Where's the catch? These two things don't look compatible.
Until now, British law has given priority to male over female heirs of kings. But where there were no male heirs, a girl got the nod.
For instance, King Henry VIII had three (surviving, legitimate) children; Edward (the youngest), Mary, and Elizabeth. Edward, the boy, was crowned king ahead of his two older sisters. He died in adolescence (without children), so his older sister Mary was crowned Queen Regnant (a female king), and when she died childless in middle age, the middle child was crowned as Queen Elizabeth I.
Centuries later, King George VI had "only" two daughters, Elizabeth, and Margaret, so the former was crowned Elizabeth II. But if Margaret had been a boy named Mark, then "Mark" would have been crowned king over Elizabeth.
Going forward, Kate Middleton's first child was a boy, but even if it had been a girl, under the newest laws, the girl would (assuming she lived long enough) have been crowned Queen (Regnant), even ahead of any younger brothers she might have had.
Britain's order of succession is determined by male-preference cognatic primogeniture (in the future it will be equal primogeniture). This allows a female to ascend the throne as queen regnant (queen in her own right, as opposed to being a consort to a king). Queens Elizabeth I & II and Queen Victoria are example of such queens. In their cases, there is no king - spouses of Queen Victoria and Queen Elizabeth II are titled "prince consort", and they are merely consorts to their queens.
On the other hand, queen consorts, such as the spouses of Kings George V & VI, did not have the same position as Queen Victoria's.
In regards the English tradition of referring to the spouse of a Queen Monarch as a *Prince Consort:
Queen Victoria (reigned 1837–1901) wanted to make her husband Albert king consort, but the British government refused to introduce a bill allowing it, as Albert was a foreigner. She instead gave him the title of Prince Consort in 1857.
Note from this that there was apparently no opposition to the title King Consort being used, only to it being held by a foreigner.
There was actually one time when England had a King and a Queen both regnant. When William of Orange was urged to come and overthrow the Catholic Stuart kings, he became King and his wife Mary, who had the blood ties to the kingship, became Queen and they ruled jointly. This situation continued until Mary died and her he became sole King.
On his death, Mary's sister Anne became Queen. Her husband was not named King, but was a Prince Consort.