Final answer:
The key obstacle that hominins had to overcome in relation to the increase in brain size was the demand for larger birth canals while still maintaining the requirements of upright bipedalism.
Step-by-step explanation:
The key obstacle that hominins had to overcome in relation to the increase in brain size was larger skulls demanding larger birth canals, even though the requirements of upright bipedalism impose limits on the expansion of the human pelvic opening. This means that the size of the birth canal was limited by the need for upright walking, while the larger skulls required larger birth canals.