Is pigment necessary to obtain white milk paint? I wanted to do some homemade white milk paint. I followed the instructions given by this website. I may have been very naive but I thought to myself that since I only needed a "whitewash" version of milk paint, then I did not need to add pigment to the recipe. Therefore I only used hydrated lime. The obtained "paint" definitely looks like in the tutorial (white version). 

But when I applied it on the surface of some clean pine plywood, instead of successfully painting it white, the wood took some strange dark tone (see picture). Now, the thing is that the surface definitely looks like it was painted, not white though. So the idea seems to at least, well, work somehow... Is a pigment really necessary to obtain white milk paint? If so, which one would work?
Yes, pigment is necessary. The milk solution creates the binder for the pigment, which is basically the mechanism to deliver the pigment to the support/surface, but it is then intended to mostly evaporate during the drying phase, leaving the pigment behind. What you're seeing now is, basically, an almost transparent darkening of the wood surface which is the remnants of the binder material.

You should be able to find dry pigment online. You're looking for, in this case, titanium white which is PW6 and it's generally available. I'm not going to give free advertising, but if you Google "titanium white dry pigment" then you'll find sources very quickly. :)