Even if exousia is active, it can refer to the man's authority in this context

Hooker and egalitarians rely on exousia being an 'active' term (woman actively has the authority). Schreiner responds: even with an active meaning, in this context it refers to the man's authority, not the woman's. 'The most sensible explanation is that she ought to wear a head covering as a symbol of man's authority over her.' Simply showing the term is active doesn't decide the issue.