Dark Matter shows up in cosmological observations as deviation of velocity of e.g. spiral galaxy arms and so on, so we know it interacts gravitational. We cannot see it, and in the Bullet Cluster you can see no interaction of the Dark Matter like the hydrogenium gas shows up - so we assume it to not interact electromagnetic. That leads up for the search for WIMPS, weakly interacting massive particles. But why do we not assume it to interact strongly?
The elementary particles of the standard model that interact strongly are the quarks, the purple ones in the plot, the interactions happening with gluons.
Note that all of them are charged, and therefore they interact also with the electromagnetic interaction. They would be seen: protons would interact with electrons in space and give off radiation , neutrons would decay into protons and electrons. Higher strong resonances are unstable and would end up into photons electrons and protons in the end. After all if you do not have hydrogen you also do not have protons.
It is only the weak interacting particles that can be candidates for dark matter.