how to have an argument while disagreeing over almost nothing.
co-pilots need to fly, obviously, otherwise they'll be gear and flap operators and nothing else. hand flying is a particularly perishable skill. come the day when the overbearing tub of lard next to them has a heart attack, they'll be useless because they've had no practice. they'll also fail their command course when its time for them fill his shoes
but, el capitan does indeed have ultimate responsibility for that aircraft (but dont for a minute think that its only HIS licence or future employability on the line) and quite rightly will allow co-pilot flying as he thinks appropriate on the day and as required by the ops manual.
on any given sector, it is the captain's privilege to decide who flys, if he doesnt care which sector he gets, then he'll ask the FO to decide, which in practice is generally what happens in my experience unless theres a sensible reason to do otherwise. If the co-pilot is getting almost no flying (as was suggested in the original post), then clearly something is not right at all... thats not the way we operate in the modern world.
also, almost all captains see it as part of their role to pass on a bit of know how to the next generation of guys, particularly the older most experienced ones who have the most to offer. the idea that you should only do that if you're being paid as a trainer is ridiculous. you learn most about flying while you're doing it for real, not doing courses or taking tests. in that sense, the captain is training the FO to be a captain.
reading some of the rubbish on here makes me realise how lucky i am to fly with the guys at my base. there are some very good young captains and also some real old timers, who have vast amounts of experience to pass on, who i respect all the more because aviation and CRM etc has changed vastly during their careers, but they have adapted.