Help understanding how to drive Step motors with Arduino
I think there is some mis-communication between you and your boss. I do not think your boss is stupid, but I do think he's talking on a different level as you do. You're using arduino which covers up a lot of hardware-interfacing, especially with steppers.
I suggest you check out this video: https://www.youtube.com/watch?v=bngx2dKl5jU
(I haven't watched it, but It will help you get more into the ideas of your boss)

Now you understand your boss's view, you can try to show him your view. When talking about steppers/arduino and how you can put in negative steps, he might think you're talking trash, as steppers require different pairs of coils to be active depending on the direction. (which is all handled by arduino)
The best way is to provide him a visual guidance, so that he can see the relation with his (hardware-view) on the issue and your software/arduino solution.

You could make something like the image below.
I'm not sure if this is what you're trying to tell him.
I guess you should mention/add that the software on the arduino takes integer values, with negative values being clockwise or such. And that the arduino will convert this to the right coil pairs or direction and step.

P.S:with direct driving, I think he meant toggling the right pins at the right moments so that the stepper will rotate, basically what the stepper library does for you. Maybe he wants you to implement something like the stepper library (is it an internship? so that you can learn?) I suggest you check some tutorials on how stepper motors work, and how you can drive them 'directly' withouth the use of libraries.