Umm..

To begin with, the universe did not begin with an explosion from a single point.

The link it points to actually doesn't say this. Sure it wasn't an explosion exactly, Big Bang suggests it did begin with a singularity.

In fact there is debate whether black holes themselves have singularities.

So? There's plenty of debates in astrophysics.

So while there are similarities between the two, we can’t simply equate them.

No shit.

The limit of what we observe (the size of the observable universe) also doesn’t match up with the hypothetical event horizon of a “cosmic” black hole.

But why does it have to?

So maybe we’re just in a really big black hole, and we just see a part of it. Not really. Just because you can calculate a Schwarzschild radius that doesn’t mean an object is a black hole.

Who wrote this? Seriously. No one is arguing that because I can calculate the Schwarzschild radius of a potato it is a black hole.

This is true in an expanding universe as well, but that’s a different story.

I'd expect this sort of writing on a toilet door.

Our universe isn’t collapsing in on itself, it’s expanding at an ever increasing rate. So it doesn’t have the necessary structure to be the interior of a black hole.

What constitutes the interior of a black hole is pretty speculative I'd day. So this isn't really saying anything.

So it’s an interesting idea to speculate about, but there is no evidence to support the idea that our universe is in a black hole.

That's what it comes down to. The astrophysicist thinks it is unlikely, so take his word for it after hearing him fluff on incoherently.