'anti-asthmatic' originates from Greek prefix 'anti-' meaning 'against' combined with 'asthmatic', from 'asthma' (Greek 'ásthma') referring to 'breathlessness' or 'a panting'.

'anti-' (Greek) + 'asthma' (Greek 'ásthma') entered Latin and then Middle English as 'asthma'; the adjective form 'asthmatic' developed from 'asthma', and the modern compound 'anti-asthmatic' was formed in modern English to denote agents acting against asthma.

Initially formed to mean 'against asthma' (i.e., countering or preventing asthma), and it has retained that core medical meaning into modern usage.