Because if you examine, you find that neither self nor phenomena have inherent existence.
That's a pretty bold claim.
How is it we can know that these things have no inherent existence?
The point is that if something is subject to causes and conditions it means it is compounded and not really inherently existent (through itself), so it can't be ultimate truth. We cannot really say how things exist, we can only say how they do not exist.
Does a thing have to be an ultimate truth to exists? Why can things subject to causes and conditions not exists? If it has a condition or can be causes to have an affect, does it not exist? If we can't know how a thing exists how could we know how it can't exist? If we can know how it can't exist, couldn't we infer the ways it can?
Basically to give you the essence, this is the middle path beyond the extremes of nihilism and eternalism.How can we know essence, how can we gain essence, how can we know we've gained it? If there are essences are there not things? For there to be an essence does their have to be a substance? How can a substance not have an essence and then have an essence by some cause?
It is not a question about whether things exist or do not. This view does not say that things do not exist. This misunderstanding comes from TC equating emptiness with nothingness, which I pointed out is wrong. To say that things are empty of inherent existence is not to say that they do not appear. They do appear (on a relative level), but only because this view is not realized (the ultimate). How do they arise exactly then on the relative level you ask? This is explained as dependent arising and there are 12 links of dependent arising which you can read about if you really wanna know.