Establishing the non-existence of an inherent self
When a cart is taken apart into all of its pieces, where is the cart? Obviously the "cart" is merely an adventitious designation that depends on all the parts being in the appropriate place.
To disprove the self-existence of the cart, as we just did, we had to know precisely what it was we were disproving - the cart. If you can come to grips with what you think something is, it is then an easy enough task to disprove its self-existence.
And this is the problem, for while we humans have no trouble defining what a cart is, we baulk at having to define what we are. Until we are brave enough to at least admit we are a thing, we will be unable to convincingly disprove ourselves to ourselves. It is not enough to realize that all the things around us lack real existence, if we cannot extend the reasoning to ourselves. If we lack the love and courage to do this, then the generative core of delusion will remain untouched, to wreak its usual havoc upon both ourselves and others.