Even if we are not managers, we may encounter many opportunities for coaching and supporting each other every day. We just rarely encounter them consciously.
Delivery-orientated coaching means showing things rather than talking about them. Coaching a team in 'advisory mode' (ie. not being hands-on in delivery) is a difficult and long path to proper agile delivery. If the team hasn’t seen what ‘good agile’ looks like, how would they know where they are heading? Hands-off advice from a coach doesn't usually help.
"Agile Coach" is an extremely overused term today: it seems like every company wants one and lots of people refer to themselves as that. At the end of the day, Agile is a means for better delivery of business value.