In spacetime there are paths of least resistance called geodesics, and an object left alone will bind to a geodesic determined by the distribution of moving masses in the spacetime. If we take two parallel geodesics in empty spacetime and draw (a section of each of) them like this ||. But let's consider if we put a massive object like a star (O) somewhere near the geodesics. We'll exaggerate in the diagrams: O<| vs |>O vs >O< vs | O | etc, depending on where we put the star in relation to the two geodesics. Note that if they are close enough, they bend towards the star.

Now we just have to bind an object to one of these ten geodesics shown schematically above.

The strong equivalence principle stems from the observations by Galileo et al. that objects of different weights and configurations fall at the same rate (if one can eliminate air drag and so on). Any object may bind to an available geodesic, whether it's a feather, a bowling-ball, a beam of light, or a moon. One has to do work to move an object off a geodesic [1].

That light binds to geodesics and geodesics are determined by proximity to mass was tested by Eddington et al. during the 1919 solar eclipse, where they observed something similar to the |>O diagram above. Gravitational lensing works the same way.

As we increase the mass of O, the closer geodesics are more and more bent towards O. So for a lighter star: |)o

Black holes are much more massive (and yet more compact) than O, so there are geodesics more bent towards the black hole (because of the mass) and and more geodesics closer to the black hole's centre of mass. The closer geodesics can be bent around the black hole, possibly several times.

Additionally there are "no return" geodesics that twist into circular orbits around the black hole. There is an innermost stable circular orbit (ISCO) too.

Finally, there are "no return" geodesics that lead past the ISCO and into the region covered by the event horizon. @ | could be a diagram where we replace O in )O | with a black hole.

Light can bind to any of these "no return" geodesics just like any other object like a feather or a bowling ball.

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[1] Strictly speaking, our universe is 1+3 Lorentzian with extremely high experimental confidence. One dimension is timelike and the other three spacelike. This lets us sort geodesics into three types: spacelike, timelike, and null (or lightlike). In normal empty space light (and any other massless particle) always moves along a null geodesic, and moving it off a null geodesic is energetically impossible. Likewise, in normal empty space, massive particles always move along timelike geodesics, and while (with a lot of work) you can move them onto timelike geodesics that look more and more lightlike, it's energetically impossible to push it onto a lightlike geodesic.

Distinguishing between lightlike and timelike is best done with respect to some coordinates, intervals, and using a tiny bit of calculus. The Euclidean distance for an object only moving in one spatial direction is ds^2 = dx^2. The spacetime interval for an object only moving in the timelike direction is ds^2 = c^2dt^2. If we let it move in the x direction, it's ds^2 = c^2dt^2 - dx^2. For light, and units of lightseconds in x and seconds in t, we have ds^2 = 0, thus "null". If ds^2 > 0, the interval is timelike. If between every two points on a geodesic the interval is lightlike, the geodesic is lightlike. If between every two points on a geodesic the interval is timelike, the geodesic is timelike: an object bound to such a geodesic does not travel as far in space over a given time as light does.

The most lightlike but still timelike geodesic is available to ultra-relativistic massive objects. So if we define an event horizon as the surface below which all lightlike geodesics lead inward, we have also forced ultra-relativistic massive objects inwards on their almost-lightlike geodesics.

Putting this more colloquially, if you are inside the event horizon, even if you could accelerate to the speed of light, you aren't getting out.