I have to agree with saddest aviator. Of course it is part of your job to train. You are a Captain and therefore a manager. Part of those functions are to impart your knowledge and experience to the team of people assigned to you. The most significant part of that team being your co-pilot.
Just as you did (and still do now hopefully,) you start at a point and grow into the type of Captain and manager by the experience you learn out on the line. Trainers are tasked with putting a solid skeleton in place, that is itself strong and reliable. Most of the meat that is placed on that skeleton is acquired out on the line, where the individual will spend 98% of their operational annual existence.
There are few things more professionaly pleasing, than seeing somebody grow into a good solid Captain. The reward for your effort being their success and any small part you played in that.
Saddest Aviator: I don't know what company you work for, but in the one where I work, 70% of F/O's already think they know a lot more than the Cpt before they reach 500 hrs.
Good! I want them to think they know more than me. I want them to question something they see as wrong. Rarely a week goes by in most pilots working lives where they don't omit or forget something, albeit usually something minor. The symptoms you describe are very common in young people. It is a part of that same teaching function, to shape this exuberance and keenness into something more consistant and workable.
I have been a Captain for the last quarter of a century, but I still remember the Captains who took the time, and displayed the necessary patience, to help me to become the Captain that I did. There were a few who
did the job they were employed to do and nothing else,
however they weren't in fact doing that at all, and in any event they are remembered, if for nothing more than cautionary examples of the trade.
If you think you only learn from trainers you are seriously deluding yourself. The advent of modern training philosophies and better awareness of integrated concepts (CRM etc.) mean that the trainers may have a fraction of your own experience, and they would be the first to admit that the bulk of what you learn and experience will occur outside of the formal training environment. Their job is to operate within that formal regime, but your development will occur in the day to day line flying.
It is therefore essential that you train. Often that means little more than allowing the F/O the lattitude to make their own mistakes and correct them. The variation of experience levels, personality, and all the other dynamics means there can be no formula for this. It will change by the day, but the day you stop being involved, and stop trying to assist the other person, is the day you really should give up.
They make you a Captain for a host of reasons, and because you ticked a lot of boxes. They never did it so that you could do "what you were employed to do and nothing else"!