sist: derived from Latin "sistere", meaning "stand"
So insist means:
Stand on (doing something).
The adverb "on" has a meaning of "continuing to do something". So "stand on" means "continue to stand". If someone continues to stand for something, he/she must want it to be done very much. So insist means "demand that something must be done".
Evolution of usage
I'll go with you if you stand on.
I'll go with you if you insist.