keep one at a distance

keep one at a distance or keep one at arm's length  {v. phr.}

To avoid (someone's) company; not become too friendly toward.

Mr. Smith is kind to the workers in his store but after work he keeps them at a distance.

Betty likes Bill and is trying to be friendly, but he keeps her at arm's length.

Compare: KEEP ONE'S DISTANCE, HOLD OFF (1a).