'insist' originates from Latin, specifically the word 'insistere', where 'in-' meant 'on, upon' and 'sistere' meant 'to stand'.

'insistere' passed into Late Latin and then into English (via Middle French or direct Late Latin influence) as forms like 'insisten' and eventually became the modern English word 'insist'.

Initially it meant 'to stand upon' or 'to stand firmly (on something)'; over time it evolved into the sense 'to press or demand firmly' and 'to state firmly and persistently', which is the modern meaning.