Because then it's not you thinking. It's Descartes' Evil Demon. The "people" in the book I write do not "think", they are writing in a book.
Thus, if anything acts on me, that is not me, so as to *try* to fool me that I am acting (not them), then "myself" does not experience it as me acting, but as someone acting on me.
Proof of this is already available. Have someone move your arms. You may have partial feeling you are moving, but also have partial feeling they are moving you.
Thus if I suggest I do not exist while existing (suggest Descartes' Evil Demon can exist) I hit a paradox in statement due to making a *wrong* assumption. If I take the assumption away, and instead try to test Descartes' Evil Demon, I find out it cannot fully exist, and would be detectable in some form.