For example, Ilford XP2 noted C41 on the box instead of d96 or d76, Kodak Black and White even explicitly warned the user "Do not process in B&W chemistry" on the film roll.

Why do these black-and-white films need the color process?

For example, Ilford XP2 noted C41 on the box instead of d96 or d76, Kodak Black and White even explicitly warned the user "Do not process in B&W chemistry" on the film roll.

Why do these black-and-white films need the color process?

Edit: as pointed out by the comment, the name can be a bit confusing. Kodak Black and White is the literal name of the film I was referring to, not all black and white films by Kodak.

Below: Kodak Black and White film, the text PROCESS C41 ONLY can be seen on the box.