But is your "me" an actual entity, or is it just the process of experiencing things? And if the latter, what does it even mean for it to have a persistent identity - and does it, or is there just an illusion of one when you consider a single time slice of processing (e.g. "now").

The problem is that, just as with the outside world, we only have the perception of our own inner workings, not real understanding of them. So we are modelling "I" as an entity, and it seems useful enough for day-to-day purposes, but how accurate is it really if you get to the bottom of it?