The following is a short essay about dualism and its criticisms and about physicalism and its criticisms.
Arguments for dualism
One argument for dualism, especially dualistic interactionism, is that it is a very common sense view. Some developmental psychologists claim to have shown that dualism is commonsensical for very young children as well. This is obviously not "proof", but it suggests we should at least have a reason for abandoning dualism.
A second argument is that the mind is (or resides in) the immortal soul. Traditional Christianity, like many other religions, teaches that you have a soul which is as different from your body as water is from rock. Your body will die and then your soul will go to heaven, or hell, or who knows where. If you believe this then you practically must believe in dualism. The only way that you can avoid believing in dualism is if you accept phenomenalism, which holds that everything is, ultimately, mental.
But in any event you absolutely cannot hold that the soul is reducible to anything physical. If events in your soul were reducible to events in your brain, then when your brain stopped functioning, your soul would cease to exist.
Note that although this religious account may motivate or reinforce a religious person's belief in dualism, it may well seem altogether unconvincing to dualism's skeptics. To use this argument to convert, say, a card-carrying materialist to dualism, it seems necessary to first establish that people do, in fact, have immortal souls. And yet the card-carrying materialist is one of the last kinds of people who are going to admit to this.
A third argument for dualism goes like this: if dualism is false, we should be able to reduce mind to matter, or vice versa, or to reduce both...