Actually strength-weakness are derived from strong-weak, which are adjectives.
And no, woman is not the opposite of man; you can say they are complementary notions, but not opposites. We are discussing language problems here, not philosophy; and from this point of view, the opposite of young man is old man.
In Arabian terms the opposite of "Woman"
is "Property Owner" but in English, Man and Woman are opposites.
Opposite in this sense is not negative. Just like opposing forces, they create a balance.
The opposite of a "King" is a "Peasant"
The opposite of "Safe" is "Endangered"
The opposite of "Ready" is "Unprepared"
These are very simple concepts. They balance, they neutralize, they are opposites.
Philosophy comes in when we are upset that a man and a woman are opposites; but without both, neither is complete.
Also, don't confuse the man/woman opposition with other terms like dominate, intelligent, covered, property. These have no place in relation to people, although political misuse has happened throughout history and continues, big-time today.