adjective
aloof
uh-LOOF/əˈluːf/
Emotionally distant, reserved, or uninvolved.
The aloof woman turns away instead of returning the man's friendly smile.

Etymology
With “on” and “windward direction,” aloof originally described steering toward the wind to keep clear of shore or another quarter. Physical separation became figurative distance: standing apart emotionally or socially.
In context
it was rumored that Mu Qingge, the eldest daughter of the Mu family, was aloof and indifferent to any man.
More examples
- Her quiet manner can seem aloof to strangers.
- The committee stayed aloof from the bitter dispute.
- Despite repeated invitations, she kept herself aloof.