Why do most people think of a black hole as having an infinitely dense point (the singularity)
Einstein field equations describes gravitation of every body in the universe. Canonical solution to these general relativity field equations is Schwarzschild metric :
$$ {ds}^{2}=\left(1-{\frac {r_{\mathrm {s} }}{r}}\right)c^{2}\,dt^{2}-\left(1-{\frac {r_{\mathrm {s} }}{r}}\right)^{-1}\,dr^{2}-r^{2}{d\Omega }^{2}, \tag 1$$
This metric has one singularity which does not go away on coordinate transformation, namely when $r=0,$ limit of (1) equation becomes :
$$ \lim_{r\to 0} \left[ \left(1-{\frac {r_{\mathrm {s} }}{r}}\right)c^{2}\,dt^{2}-\left(1-{\frac {r_{\mathrm {s} }}{r}}\right)^{-1}\,dr^{2}-r^{2}{d\Omega }^{2} \right] = - \infty, \tag 2$$
So, roughly speaking space-time element at this point becomes infinite. Any two events which is seemingly very close to this singularity are separated in time by "Googolplex" time interval (joke). At exact singularity point as (2) limit shows space-time breaks at all and it's not possible to say "when" or "where" about event (if any) happening at singularity in the center.
That's why.
Caveat:
Your question makes sense in such view, that what exactly happens at the center is believed to be known when we invent fully complete quantum gravity theory. In the past quantum mechanics has eliminated some black body radiation singularities ("ultraviolet catastrophe"). So it's natural to expect that quantum gravity could eliminate gravitational singularities once again. If this will happen, maybe really at the center is not a "naked Einstein singularity", but some "quantum object" instead.
Last most intriguing scenario is that neither general relativity, nor quantum mechanics models are applicable to the singularity object. Maybe for resolution of this conundrum we need not mix relativity with quantum world laws, but to invent totally new Physics, whatever it could be. Sounds strange, but given that we are trying to merge GR and QM for almost $100~\text{years}$ with no success, this may indicate that we are going not in that direction.