side-step n.

late Old English, "long, broad, spacious; extending lengthwise," from side (n.). Compare Old Norse siðr "long, hanging down." From late 14c. as "being from or toward the side," hence also "subordinate." Also "apart from the main course" of anything, as in side-road (1854); side-trip (1911). In side-eye (by 1922) the notion is "directed sideways."

Old English steppa (Mercian), stæpe, stepe (West Saxon) "stair, act of stepping," from the source of step (v.). Compare Old Frisian, Middle Dutch, Dutch stap, Old High German stapfo, German Stapfe "footstep").

It is attested from late Old English as "degree on a scale." The figurative meaning "action which leads toward a result" is recorded from 1540s. In dancing, from 1670s. The meaning "type of military pace" is from 1798.

The warning phrase watch your step is attested from 1911 (Wycliffe, late 14c., has keep thy foot in essentially the same sense). Step by step indicating steady progression is from 1580s. To follow in (someone's) steps is from mid-13c.