be headstrong—be self-willed and obstinate:
- George Eliot’s young country hero is headstrong and arrogant, and sees the world in black and white.
have a strong head —(coll.) be not easily intoxicated by liquor:
- I could drink as much as the best of them and I had, for such a youngster, a tolerable strong head.
Note:
a) Neither expression correlates in meaning with the phrase be strong-minded—be resolute and determined:
- Everyone describes him in a similar way—to say that Clarence was strong minded, had a strong personality, was strong willed.
b) Neither expression is antonymous in meaning to the phrase
be weak in the head—(coll.) be mentally retarded (also: be soft in the head):
- When he stopped speaking his mouth hung open … I realized that he was weak in the head.