A wider tyre has more road surface underneath it that is trying to tug it every which way at once. The problem is exaggerated by the lower profile that normally goes with the bigger width - the tyre wall is stiffer and less flexible, so the twisting forces on it are not damped out so well.
If they built roads properly we wouldn't have all this grief. I took Fabrizio (my Permental 4) to Italy in 2001 and it was transformed. Back in the UK he reverted back to being the uncouth, spine bashing, unwieldy, tramlining maniac.