[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).