Sean Carroll has a nice post explaining why the universe cannot be considered a giant black hole:

If there’s any quantitative reasoning behind the question (or claim), it comes from comparing the amount of matter within the observable universe to the radius of the observable universe, and noticing that it looks a lot like the relationship between the mass of a black hole and its Schwarzschild radius. That is: if you imagine taking all the stuff in the universe and putting it into one place, it would make a black hole the size of the universe. Slightly more formally, it looks like the the universe satisfies the hoop conjecture, so shouldn’t it form a black hole?

But a black hole is not “a place where a lot of mass has been squeezed inside its own Schwarzschild radius.” It is, as Wikipedia is happy to tell you, “a region of space from which nothing, including light, can escape.” The implication being that there is a region

outsidethe black hole from which things could at least imagine escapingto. For the universe, there is no such outside region. So at a pretty trivial level, the universe is not a black hole.