I'm not an expert on particle physics, but the verbiage sounds to me like one of the standard problems in physics: We can write the differential equations. But even simple differential equations can be unsolvable. For example, consider the simple Three Body Problem. The differential equations are simple enough that you can use them as an introduction to the concept of differential equations themselves, but the Three Body Problem is not in general solvable.

The three body problem can generally be acceptably approximated for a reasonable period of time. But that problem only involves inverse squaring of distances. Strong forces decay much faster than that, which makes them more sensitive to errors. Plus you end up with one of the fundamental problems we have trying to understand our universe, which is just how monstrously enormous and monstrously slow we humans are. We operate at "meter" scales and "second" time frames, and particle physics operates at somewhere around 30 and 40 orders of magnitude smaller, respectively. (Not quite all the way down to the Planck sizes, but closer to those than to the macroscopic world.) So when you try to numerically approximate the differential equations, you don't get very far in time or space before your approximations have critically diverged from reality.

It's like we're trying to work out the fundamentals of chemistry and our primary tool is smashing planets together.