'To back down' definitions:

Definition of 'To back down'

From: GCIDE

Back \Back\, v. i.
1. To move or go backward; as, the horse refuses to back. [1913 Webster]
2. (Naut.) To change from one quarter to another by a course opposite to that of the sun; -- used of the wind. [1913 Webster]
3. (Sporting) To stand still behind another dog which has pointed; -- said of a dog. [Eng.] [1913 Webster]
To back and fill, to manage the sails of a ship so that the wind strikes them alternately in front and behind, in order to keep the ship in the middle of a river or channel while the current or tide carries the vessel against the wind. Hence: (Fig.) To take opposite positions alternately; to assert and deny. [Colloq.]
To back out, To back down, to retreat or withdraw from a promise, engagement, or contest; to recede. [Colloq.] [1913 Webster]
Cleon at first . . . was willing to go; but, finding that he [Nicias] was in earnest, he tried to back out. --Jowett (Thucyd. ) [1913 Webster]