"The self" is just a other way of saying "the unified stream of experience". It is not an illusion, just a fact. No one has ever experienced two consciousnesses. The term "the self" is simply a way of stating that fact.
That's the whole mystery right there isn't it? No one has ever had a solid explanation for the apparent unity of the stream of consciousness. I suspect it has something to do with the composition of oscillatory patterns, similar to a sound wave being a combination of many individual sounds which get combined through wave interference into a unified pressure wave. But that leaves many questions unanswered. Better to be puzzled by this than assume we should know the answer right now. We just don't.
