I would probably use one of colors of either the bathroom or hallway.

He's right about using a light color in a closet. Even if it had a window in there, you need all the light you can get. An antique white would be nice. It won't be glaring like white, but it will help him see his clothes better.

A creamy white would look great with your green walls.

I agree....the lighter the better, esp with the dark wood in there already.

Would pointing be ok?

Yes.
Pointing is a great color.
You might even go up a bit to Wimborne White.
And do be sure to have plenty of pure white light that falls on the clothes. Otherwise, you miss little spots and linty bits and mismatched colors and other things that show up in daylight.

My thought is that all closets should be white because we change the bedroom wall color and want to leave the closets alone and white is such a clean color.

Light/white works well for closets so you can see what's in there and see the colors clearly.

Thanks for the motivation threeapples! You spurred me to start a closet painting project this morning. I used to paint closets to match the room but now I paint them white. Only the MBR has lighting so it really helps see what is in them.

I'd go up a shade from Pointing. In a small room Pointing will give off too much yellow I think.

What is a shade up from pointing? Shaded White?

I have no idea what the next shade is, I'm just saying all you need is a creamy/antique white that you can buy almost anywhere.

But since it's a small area I think Pointing would be fine, except it will have a yellow hue. Smaller areas are more intense than a large wall, that's why I'd go with an off-white of some sort.

If I were you, i would choose a off-white to make the space look bigger

Farrow & Ball doesn't really work that way. There is no "one shade up" really.

I don't think you can go wrong with Pointing, I'm a huge fan and think it's the world's most perfect white. It's undertones are primarily red, not yellow, but who knows what it will do in your space. It's always wise to test F&B in situ.

White Tie is also lovely, but very much an ivory. Dimity is pinky. I've misplaced my fandex so I cannot help much with the other whites. But the F&B whites are great;;;