Many years ago, my grandfather told me it was because trees were splitting their bark.
The thought was that trees in the woods had brush and other trees to shield their bark
from direct sunlight. As people cut down trees and built houses, the bark became exposed
and didn't like the direct sunlight. People painted them white to reflect the light.
I have also heard that trees that grew up without anything shading their trunks
didn't suffer the way trees that were already grown did, which may explain why
the practice is fading. Or, it could be it really did nothing to protect them.
I went to a college that used to mow around all of their trees, like you would expect.
Until I started going, and they stopped mowing within 10 feet of all the trees.
The story I heard was that old trees started dying, and a biology professor said it was
likely due to the mowing. (I say bullshit, but I'm not a biologist)
Regardless, now with tall growth on campus, the biology students actually have stuff to
study other than Kentucky Bluegrass. Now they have poison ivy, and dandilions, and
all kinds of thorny bushes. Dumbasses. At least the rabbits and squirrels have a place
to hide.