stile: [OE] A stile is etymologically something you ‘climb’. The word goes back ultimately to the prehistoric Germanic base *stig- ‘climb’ (source also of English stair, stirrup, etc, and of German steigen ‘climb, rise’). => stair, stirrup
Old English stigel, stile "device for climbing, ladder," related to stigen "to climb," from Proto-Germanic *stig- "to climb" (see stair). An arrangement to allow persons to pass but not sheep and cattle.