As far as I understand the discourse is more subtile than 'no self exists'. There is no claim that 'no self' exists because something obviously exists, we are here, so self exists in all of us and this self is similar to what in Hinduism is called Atman (the universal self). However buddhists argue that no individual self exists, that our individuality (ego) is an illusion because it is impossible to separate your self from other beings. A good example is your hair - when they grow we cut them off and there is this magic moment where mentally we change our perception from hair being 'me' to 'not me', but this separation line we draw is very abitrary and in some states of consciousness it is possible to see that this line does not exist at all.