con-: together, with
sist: derived from Latin "sistere", meaning "stand"
-ent: of doing something
So inconsistent means:
Of not standing together.
If someone's statement/behaviour does not stand together with before, this means "its statement/behaviour changes so that other people become confused".
Evolution of usage
The statement of not standing together will make people confused.
The statement of not consistent will make people confused.
The inconsistent statement will make people confused.