My own reason is that training for strength stimulates your body to produce testosterone, which stimulate logical thinking, among other things.
Low level of testosterone found to be one of reasons of men's depression.
Low level of testosterone found to be one of reasons of men's depression.
It has the additional benefit that it alters your mood, aerobic exercise makes you happy :)
Strength training may boost testosterone, but the effects of aerobic exercise is well established. Several comparisons have been done between aerobic and strength training and the conclusions have been that strength training have little effect on executive function.
My source for this is the book "Brain Rules" by John Medina [1]. Also check out his presentation on exercise [2] and his Authors@Google talk [3].
[1] http://www.brainrules.net [2] http://www.brainrules.net/exercise [3] http://www.youtube.com/watch?v=IK1nMQq67VI
(Thanks for the citations. That's awesome, and I wish more people would do it.)