Central egalitarian claim: hosting a house church made you the leader/overseer of that church

The claim appears repeatedly: if a woman hosted a church in her home, she was therefore the leader (overseer) of that church. Belleville calls Mary, Lydia, and Nympha 'overseers of house churches.' The word 'overseer' is a biblical term synonymous with elder and bishop. Mike notes this is a massive claim worth investigating.