The reason is because foam is made out of tiny little bubbles. The bubbles refract the light in a way that makes it look white.
A great example of this effect is in white candy. White candy often does not use food dye, but is instead clear candy that is folded a bunch of times to trap little air bubbles. [Here’s a video of it in action](https://youtu.be/qZohC_UUdE4?t=167)
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