As others mention, it's the coaxiality of the diameters that's missing as well as the location of the 'flats' relative to the diameter. You could add controls, or if it meets your functional requirements add a drawing note something like "PERFECT COAXIALITY AND LOCATION OF SYMMETRICAL FEATURES AT MMC REQUIRED FOR RELATED FEATURES" (you can tell your boss this comes from ASME Y14.5M-1994 section 2.7.3).
Not to mention what a particular machine shop will need, or use
A basic principle is to generally make the drawing so any competent machine shop can make an acceptable part to it. Now there is the odd exception in cases of IP or uncommon processes etc. but if you don't control what machine shop it gets sent to, then the drawing needs to document it such that any competent machine shop can make the part.
These pins have been made, on more than several occasions before, from drawings with less detail than what I have on mine and ALL of them fit perfect.
Just because you've had a few made to crummy drawings that are OK, is no guarantee that the next batch will be OK, especially if you have to go to a different shop. In the US & UK the general philosophy is that you dimension a drawing to essentially show what you will accept. You want the drawing to not allow any non functional parts, while at the same time not unnecessarily rejecting parts that are functionally OK but don't meet inappropriate drawing requirements. If you have a crummy drawing that doesn't give explicit requirements then you may legally be forced to buy crummy parts.
If you are in the US then he's probably expecting you to use ASME Y14.5. However, the question still stands of which edition. There are differences between edition as the standard has evolved over time, so you should ask what edition and if the company has a copy you can look at.
Try and get some training if you can. There are even some purveyors of self paced computer based training though I think it's only for the basics. There are online resources available too, you've just found one good one, here's another that has some stuff
and another
However, the relevant standard is the 'bible' most trainers and authors of GD&T books and even folks on this site have their own idiosyncrasies (probably including me) so always go back to the source documentation.
Your manager seems a bit harsh, but then again so was my first boss and I ended up learning a bunch from him and I turned out fine (or some might argue not;-)).
Posting guidelines faq731-376 (probably not aimed specifically at you)
What is Engineering anyway: faq1088-1484