The ability to run long distances and sweat—so as not to overheat, allowed our ancestors to wear out other animals. Sweating was the key factor. Consider a gazelle running over long distances and being chased by our progenitors. The fact that they can sweat and the gazelle can’t means they can last far longer in the heat of the African Savannah.
Game animals like the gazelle over time become overheated and have to stop to catch their breath, allowing early hunters to make short work of them, a strategy we call today persistence hunting. After about five miles or so, a gazelle needs to stop, rest, and breathe, or risk damaging itself, even dying. Such an animal can only fully extend its diaphragm when not running, while walking upright freed our ancestors from such an issue.