Green’s Dictionary of Slang

go-around n.

In phrases

give someone the go-around (v.) (also give something the go-around) [var. on give someone/something the go-by under go-by n.]

of a person or thing, to reject, to avoid, to jilt.

C.H. Spurgeon ‘A Singular But Needful Question’ Sermon No. 955, delivered on 16 Oct. at the Metropolitan Tabernacle, Newington, at SpurgeonGems.com 🌐 Be considerate, I pray you, concerning the first and chief question. Do not give it the go around. Your dying hour may be much nearer than you think.
[US]J.A. Russell ‘Colloquial Expressions from Madison County, NY’ in AS V:2 152: To give the go-around: to avoid a person.
[US]in DARE II 699/2: Qu. II5b, When you don’t want to have anything to do with a certain person . . ‘I’d certainly like to give him the _______’ [...] Go-around. Qu. AA11, If a man asks a girl to marry him and she refuses, you’d say she _________’ [...] Gave him the go-around.