But your answer also goes beyond that. You're asking why it's
so much stronger
In other words, it's not twice as strong, nor ten times as strong. Relative to EM, it's about 100 times as strong, and compared to others it's several orders of magnitude. You could also pose it in another way: "why isn't the Strong Force 100 thousand times stronger than electromagnetism?" In other words, what you'd be asking is whether it's possible to have the theories explain the *strength* of the interactions.
Again: I'm not answering your question, I'm giving you more "food for thought". Science is not only about knowing stuff, it's also about getting an attitude of asking questions that *might* lead to a plausible answer or explanation.
On one hand, the "strength" of the interaction between two particles has to do with the number of ways they can interact. You can think of it as counting Feynman diagrams. But remember that you can draw diagrams with an arbitrarily high number of interactions (many loops), so that too doesn't cut it. In fact, the "weight" of each diagram is tied to the coupling constant for each interaction; and it's that coupling constant that is more significant for the strong interaction than for the others, with a provisio: it is evaluated at a given energy range. That's why there's a thing as "running constants". http://en.wikipedia.org/wiki/Coupling_co…
(I'll note, on the subject or "renormalization", that it has to do with rewriting the equations in a way where you always get the maximum probability equal to 1, representing absolute certainty, and the minimum probability equal to 0, representing absolute impossibility. It doesn't make sense to think of a probability of 200% any more than it makes to think of 1+1=3.)
There are unification theories that make a prediction that the strength of the interactions vary with the energy scale at which you're considering the interactions, and that their relative strengths converge to a high energy scale, the Planck scale.