Edit: People are confusing [this concept](https://en.m.wikipedia.org/wiki/Innermost_stable_circular_orbit) with the [Roche limit](https://en.m.wikipedia.org/wiki/Roche_limit). Wikipedia isn’t very helpful in explaining why the innermost stable circular orbit exists, but it does lay out the basic concept. It’s the innermost point at which an object can orbit another object at all, not the point at which it begins breaking up from tidal forces.
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The issue is that within a certain distance (for non-rotating black holes: the event horizon), the geometry of space(time) is so warped that _all_ directions lead inwards. So regardless of what you do, it will bring you closer to the center, which is ultimately in every direction. In particular, no orbit (stable or not) can exist, as an orbit would lead back to its starting point.
That shows that within some distance, there is no orbit (stable or otherwise!), not even a closed loop. However, one can show that even somewhat further outside there cannot be a stable orbit. The reasons are similar to the above, but more convoluted; let me try to at least argue intuitively that even slightly outside the event horizon of a non-rotating body, there is still no stable orbit:
The closer you get towards a black hole, the more directions lead inwards, until finally all of them do at the event horizon. Slightly outside of it, the only directions not pointing inwards are (almost) directly away from the mass. Hence any orbit would need to go in that direction to even have a chance to loop. But now imagine what it looks like at the end of the first orbit: you would arrive from the backside of your initial direction, i.e. from where the event horizon is. Which clearly cannot happen, as nothing can escape it (again because all directions are inwards).
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