The big bang was given it's name by Fred Hoyle, in order to make the theory sound absurd.  He metaphorically called it an explosion.   In the mist of time most people even some scientist lost the metaphor part of that and thought of it as an explosion.  Others then stopped using the metaphor because it confused people.
This is more of an entry about the use of language than physics.  That said here is the shortest possible argument for why the big bang was not an explosion for anyone who needs convincing:

Explosions are the free expansion of material from higher, pressure, temperature and density to lower pressure, temperature and density in a short amount of time.

The big bang was the expansion of the space time manifold from a singular point at time equals zero to a four dimensional manifold growing with time.  In the process the contents of the universe expanded to fill the new space that was created after the big bang.

The big bang was not an explosion because no matterial was involved.  None existed yet. The big bang was the sudden expansion of space-time.  That is not the same as an explosion in any physical sense.

That said in terms of the accurate gramatically correct usage of the language in the sense that any English teacher would agree with writing the big bang "was" an explosion is correct.

What's in a name?

How many times in the last few weeks did someone say "tidal wave" only for someone nearby to say.  "They don't call them tidal waves.   They aren't called tidal because there is no tide involved.  They are called Tsunami's!"  (subtext... that the person saying "Tsunami" is smart")

Odds are the person saying Tsunami has no idea that it literally means harbor wave.   Well, being really literal about it only a wave that hits a harbor is a tsunami.  Therefore that person is no more correct than the person they were seeking to belittle.
Even more I like the way that Richard Feynman puts it here.
TLDR:
In terms of physics the big bang was not an explosion it was the expansion of space time.  In terms of the rules of the English language the closest metaphor for the event is to call it  an "explosion of space".  Just don't confuse that for the physics.
If you want to be a stickler for physical correctness then say that the big bang is this.
$ds^2=-dt^2+a^{2}(t)\left[\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2Sin^2(\theta)d\phi^2 \right]$

a(t) grows with time and causes three dimensional space in the universe to grow with time.  The beginning of this process at t=0 was the big bang.