'V3' yr instructor was correct with regards to yr first couple of lines in yr post.
"5-in-50" said ti well but here's anther way of looking at it.
Look at it this way. You pass abeam a station by say a mile or so, it's irrelevant anyway the distance. Seeing as yr still close in notice that the needle head drops fairly quickly at first towards the bottom of the compass card. But as you get further & further away from the station that rate of change (towards the bottom of the card) slows, that's providing nothing else changes in a windless perfect tracking environment. Look at it like the spokes on a wagon wheel they are close together at the hub (the radio beacon) & way out near the outer ring of that wagon wheel (a theoretical never ending ring limited only to radio range)the spokes are a long way apart so it takes longer for the needle to drop or transit between spokes so to speak assuming each spoke is one degree for Eg.
That's the way I see it & most likely yr instructor
Wmk2