'anti-skeptical' is a compound formed from the prefix 'anti-' (from Greek, where 'anti-' meant 'against') and the adjective 'skeptical' (from Ancient Greek 'skeptikos', related to 'skeptomai', 'to look, to consider').

'skeptikos' (Ancient Greek) passed into Latin and then into English as 'skeptic'/'sceptic' and 'skeptical'; the productive prefix 'anti-' (Greek) has been attached in modern English to create compounds such as 'anti-skeptical'.

The constituent parts originally conveyed 'against' + 'looking/considering'; over time the compound came to mean specifically 'against skepticism' or 'not inclined to be skeptical', i.e., opposing doubt or critical suspicion.