The other person is likely thinking about the concept of escape velocity. There are people who claim no man-made spaceship could ever have gone into space because they cannot reach the escape velocity for the earth. What they fail to acknowledge is that the escape velocity for the earth is not a constant, it depends on how high above the surface you are.
So what you do to get into space is to reach the escape velocity at the height above the surface you are at. This is in practice obtained by maintaining an energy output until $v(t) = v_{\text{escape}}(h)$ where $h = y(t)$ is the vertical distance of the spacecraft to the earth's surface at time $t$. (see also this answer) When that condition is fulfilled, no additional thrust is needed and the spacecraft will escape the earth.
However, things are different in the case of a black hole. Within the event horizon the (timelike) geodesics of Schwarzschild spacetime are closed curves leading inevitably to the singularity at $r=0$. A clear picture is painted by the Kruskal spacetime diagram:
Here, the event horizon $r=2GM$ is a diagonal line bisecting the right angle between the Kruskal coordinate axes $X$ and $T$ and the singularity $r = 0$ is contained within the blue region marked $II$. The benefit of using Kruskal coordinates to describe Schwarzschild's spacetime is that (radial) light cones are defined by $X = \pm T$ and therefore the causal structure of spacetime is very clear.
Indeed, any observer inside the blue region of spacetime is doomed. Their light cones are completely contained within this region and the singularity is unavoidable. Another interesting way to see this is by simply looking at the Schwarzschild metric:
$$ds^2 = -\left(1-\frac{2GM}{r}\right) \text{d}t^2 + \left(1-\frac{2GM}{r}\right)^{-1} \text{d}r^2 + r^2 d\Omega_2^2$$
where $d\Omega_2^2$ is the metric on a unit two-sphere (don't worry about this part, it contains angular coordinates only and we're interested in radial curves, i.e. curves without angular dependence).
Shamelessly ignoring the coordinate singularity at $r=2GM$, let's see what happens on either side of the event horizon. We notice that for $r>2GM$ this metric has signature (-+++). But when $r<2GM$, the factor in front of $\text{d}t$ becomes positive while that in front of $\text{d}r$ becomes negative. So for $r<2GM$ the time-coordinate becomes spacelike and the space-coordinate becomes timelike! Thus you can no more stop yourself from moving toward the singularity than you can stop yourself from getting older.
Outside the event horizon (region $I$ in the above diagram), a (Schwarzschild) black hole behaves like any other celestial body and you can perfectly well have stable orbits and talk about escape velocities in this region of spacetime. But inside the event horizon there isn't even a notion of escape velocity, since it is defined as the velocity needed to reach infinity without additional forces and everything inside the event horizon is completely cut off from spacelike infinity.
