Well, do they not "throw logic out the window" when they talk about "love"?
no, love makes very much sense when you examine it. people feel "love" because they are genetically programmed to. it promotes survival. this does not explain away all of loves illogicality, but you can at least say "yeah, I can see how love might arise as a strong influence on our actions"
Do they not "throw logic out the window" when they tell young teens to abstain from sex?
no, they know it may not work because the hormones in teenagers are telling them to have sex, but they try anyway in a struggle to promote their values. that is not illogical, its simply the best method available.
I would say that most, if not all, humans exhibit that very trait in varying degrees. And religious leaders are, after all, human, are they not?
by saying they exhibit these traits, I imply that they posses them with a greater magnitude than average. similarly, saying "wow that person is energetic" does not simply mean that they use energy, as all human so, but that they use an exceptional amount.
returning to my original point, it is no so much the illogicality of religion that bothers me, as love is still fairly illogical and yet does does not bother me, it is the way that illogicality seeps from people's personal beliefs into all matters. religious doctrine has evolved over time to control people, and to reject what might be objectively more beneficial thoughts and actions, and replaces them with the ideology of whomever was fortunate enough to have their doctrine catch on. in short, it replaces original thoughts with the thoughts of those who write doctrine.
the above is pointed at most mainstream religions, as some do not operate this way.