The ability to perform both strength and endurance exercise has been honed through many years of evolution. Each endeavor relies upon different biochemical specificity and trade offs, so it may be not only difficult but contradictory to have maximal ability in both. An analogous comparison is the competition for resources between exercising locomotor muscle and the pulmonary musculature.
During intense aerobic physical activity there is an increase in blood flow into the locomotor muscles which are doing the active task. Obviously, if you are running there will be very little need to perfuse/oxygenate the forearms. However as you need to increase the fuel supply(O2), the respiratory system needs to work harder to provide it. The rate of respiration, and volume of each breath will increase. Since this respiratory boost is accomplished by muscular effort, the body needs to make some choices in what to focus on, the exercising muscles versus the pulmonary musculature involved in the work of breathing.
This is not an easy choice on first glance. Obviously if we neglect the lung muscle function(more to the legs for example), the oxygen and CO2 transport will suffer leading to issues with locomotor muscle performance and systemic hypoxia. On the other hand being too generous toward the respiratory system could take away resources to the working muscles preventing a faster run/bike/swim. This interplay between pulmonary and locomotor blood flow and substrate use has been investigated with some fascinating results. For example, a study was done comparing the muscle O2 drop(vastus lateralis and intercostal) from forced hyperpnea (rapid breathing attempting to make the resp muscle work harder) vs the O2 drop with a cycling ramp test. As seen below, the O2 did decrease as expected in the VL, but actually did an even greater drop in the intercostal area. There was no real change with forced breathing.
In summary, the intercostal muscle O2 drop was profound and even larger than the typically measured leg muscle in cycling.
Another way to look at the situation between competing muscle groups is to either load or unload one group and see how the other group performs. This is what was done by this study that looked at quadriceps force after a 300 watt cycling interval under three conditions. The subjects were either breathing through a resistive load (increase work of breathing), a respiratory unloading device (less work of breathing) and control. As imagined the quad peak force was diminished by the resistive load (and time for interval completion reduced). However, the unloading device actually improved the post exercise quad force from control. From the paper:
Another key finding was that perceived exertion in the legs as well as dyspnea (short of breath) was less with the unloading trial and higher during the respiratory load: