Egalitarian interpretation of Ephesians 5:21 as umbrella of mutual submission

Egalitarians read 'submitting to one another out of reverence for Christ' (v.21) as meaning everyone submits to everyone equally. Then 'wives submit to your husbands' is just an example of what everyone does. Husbands love is also submission. The result: no authority difference. Mike argues this creates an impossible dual-messaging: Romans would read wifely submission while Christians would read mutual submission from the same text.