No one is denying neurological processes taking place. Just because a car moves forward because of its wheels, pistons, axle, engine etc......doesn't mean there is no driver.
You agreed that the idea of a Self is 'overwhelmingly compelling'....so you should say why it cannot exist.
I'm not saying it cannot exist, more that there is no evidence for it, or at least none for a primal ontologically distinct thing, inside us, which is sort of how it feels. What the evidence does suggest, is that we develop a
sense of self in terms of a unitary focal point of volition, agency, memory, experience and so forth which persists over time thanks to the fidelity of cell replication. We can infer complex processes going on under the hood to create this sense by examining cases where it breaks down - people with xenomelia, body dysmorphia, or amputee syndrome for example, these are outcomes associated with an underperforming sense of self.