At least, if you teach the real theory (called Big Bang by Fred Hoyle in 1949 -- Fred was an adversary of the theory).
All the theory does is to claim that the expansion of space has an effect on the energy content of the universe:
Same total amount of energy + more space to spread it out = the energy density goes down with time.
Conclusion: the universe cools as space expands.
The theory was published in 1948 and, immediately, everyone tried to prove it wrong (this is what we all do about all theories - since they come out hundreds at a time).
It survived the first year (which is already quite rare for a theory).
Fred Hoyle was a very famous astrophysicist. He was also a proud atheist; he claimed that being atheist made him a better scientist. He was very much against the idea (and the mathematical model) behind the 1948 theory, mostly because it led to the idea that the universe may have had a start - a "moment of creation" (the ideas and mathematics behind the 1948 theory were from a priest).
Fred published his own theory in 1949 and named it "Steady State". The other theory did not yet have such a catchy nickname. During a radio interview, Fred came up with "Big Bang" as a way to make fun of the 1948 theory. Unfortunately, the name stuck (it gives the false impression that the theory includes an explosion, which is does not). In Steady State, the energy density remains constant despite the expansion of space; the Steady State universe eternally remains at the same temperature.
All the rest of what Big Bang includes is simply the application of known scientific principles to the energy of the universe. For example, it is well known from lab experiments, that hydrogen gas hotter than 3000 degrees is not transparent (that is because the heat keeps knocking the electrons out of their orbits around the protons - and free charged particles love to interact with light).
Since the Big Bang theory claims the universe was hotter in the past, then the theory "predicts" that the universe only became transparent when the "temperature" (the energy density) went from above 3000 to below 3000.
Sure enough, with new radio-telescopes in 1964, the evidence (Cosmic Microwave Background radiation) showed that there was a moment (over 13 billion years ago) when it happened. Under Fred's "Steady State", this is impossible.
That is simply application of known scientific knowledge. As such, there is no controversy.
Controversy occurs when someone tries to teach Big Bang as a model of "Creation". The theory says nothing about creation, as it cannot go back beyond what we call the Planck Time (when the Observable Universe was already in existence and space was already expanding). IF (a big if) there was a "Creation", it happened before the earliest moment that can be analyzed by Big Bang.
Unfortunately, the priest who had come up with the ideas DID write that Big Bang represented how the universe bahaved right after [his] God created the universe.
Or worst: "Creationists" wanting to discredit the Big Bang theory, teach it all wrong on purpose, then claim that it is therefore impossible. They just continue the atheist work that Fred had started.
Thus teaching THAT version of Big Bang is also controversial.
There are still things about the universe that don't quite fit with the Big Bang theory. So far, they are just "annoyances" (they don't prove the theory to be wrong -- we simply do not know how to fit them in the theory). Things like Dark Matter. Until we find out what Dark Matter really is, then we will either be able to fit it in or... we will need to fix or replace Big Bang with a better theory.
Teaching that Big Bang is "perfect" would be controversial. It is not perfect. It is simply (for now) the most useful tool we have to understand how the universe behaves.