Descartes wanted to believe that the mind was something special and separate from the matter that makes up our bodies. After all, if the mind is of the same stuff as the rest of the universe, how can you defend the idea of free will from charges of determinism? So he came up with some arguments supporting dualism, the world view that the mind and the body are intrinsically different from each other. Here is his first attempt:
(1) I am not dubitable -- See The method of doubt.
(2) My body is dubitable
(3) I and my body do not have exactly the same Intrinsic properties
(4) If I am the same thing as my body, then I and my body have exactly the same intrinsic properties.
Therefore (5) I am not my body
The problem with this argument is that doubt is not an intrinsic property. It is projected by the doubter. Therefor this argument is not sound.
Next Descartes tried replacing dubitable with divisible. You can cut off a finger and have 'two parts of your body'. You cannot cut off a piece of your mind and have two parts of your mind. The problem with that is that you can cut off bits of your mind. A lobotomy, for example, will result in two parts of your mind that do not always work together and may be unaware of what the other is doing. We also may loose part of our mind (the ability to speak, to comprehend, to taste or see, to plan, to remember, etc.), which means that these parts of the mind are indeed divisible. However, this objection was not made apparent to Descartes, so he remained satisfied with the philosophy of dualism. But now you know better!