leaving it to one's man; entrusting to one's husband/boyfriend
Often used when a woman leaves a decision or task to her male partner, sometimes with a nuance of relying on him or letting him take charge.
She leaves the household finances up to her husband.
When she left the trip planning to her boyfriend, they couldn't decide on a destination.
Compound of 男 (man) and 任せ (leaving to, entrusting).