With monotheism, we have two main assumptions about a personal god. First of all, he must be omnipotent. He must be able to control everything, all the time, and be able to break the laws of physics whenever he wants. This is important for him to be "personal" and be a part of everyone's lives and enact his "plan". He also needs omnipotence in order to create the universe. The second assumption is that he cares about humanity and controls its destiny in a non-malevolent fashion. This one is more obvious, being that he is the personal god depicted in Christianity.
The logical contradictions here should be obvious now that I have laid out these two features of a personal god, but allow me to point them out more thoroughly. First of all, omnipotence itself is self-contradicting. In the classic example of "what would happen if an unstoppable force met and immovable object?", omnipotence is logically impossible. What if this omnipotent god used its magical powers to create a rock so strong that even he could not break it? If there was some rock that this god could not break, would that not mean that it is not omnipotent?
Furthermore, there is the fact that our world is obviously not controlled by an omnipotent, non-malevolent god. An omnipotent god that truly cared about his people would not even allow evil to happen. Assuming that, in Christianity, all of the acts on the ten commandments are "evil", how could such a mighty god even allow these acts to exist? Does he see people murdering each other and stealing from each other and just shake his fist at them from the sky? That does not sound like something an omnipotent being would do.
Some might say that he does not interfere for the sake of free will. In the example of Christianity, this excuse is hardly worth noting. It is a sin in the religion of Christianity to disbelieve in their god. Once again, the god does nothing to prevent the terrible evil of other religions existing and of atheism existing. You cannot say that your god gives you free will without sacrificing either his good will, or his omnipotence. And you cannot say you believe in a personal god without sacrificing logic.