Old English 'withutan' — 'with' (against) + 'utan' (outside); 'lacking' developed as the spatial sense faded.
From Old English 'wiþūtan,' a compound of 'wiþ' (against, toward, opposite, facing) + 'ūtan' (outside, from outside), itself derived from 'ūt' (out). In Old English the word was primarily spatial: 'wiþūtan' meant 'on the outside of' a physical boundary — outside a wall, a building, a city. The modern sense of 'lacking, in the absence of' developed during the Middle English period as the spatial metaphor generalized: to be 'without' something is to be on the outside of having it. Old English 'wiþ' (the first element) is cognate
In Old English, 'without' meant 'outside' — purely spatial — while 'within' meant 'inside.' The pair formed a perfect spatial antonym. When 'without' shifted to mean 'lacking,' English lost the clean opposition and had to press 'outside' into service. Scots English still preserves the old spatial 'without' in the word 'outwith,' meaning 'outside of.'