Competition can be asymmetric in two ways.
It may be more expensive to enter into direct competition for one side of the competition. Due to cost of changing resources to acquire or imitate needed resources. A chain of ice cream kiosks may introduce a line of exotic flavors, and a fast-food chain may do so easily as well (assumed they were also serving some kind of ice cream). But the chain of ice cream kiosks will need much larger effort to match a new offering of burgers from the fast-food chain.
One company may be a competitor for the other company, but the vice versa is not true. Competitors are companies that share the same markets and resources but the overlap itself may be asymmetric. For example, Company 1 has resources A, B, C and targets markets X, Y, Z; Company 2 has resource A and targets market X. Therefore, Company 2 is much less a competitor to Company 1 than what Company 1 is to Company 2.