I don't understand what Q's objection was to the human race, specifically. In Encounter at Farpoint, Q's specific target for ire is humanity. From what I've seen in all of Star Trek, Humans are no different than any other species in the galaxy when it comes to morals, goals, ambitions, desires, manifest destiny, etc...
The original intent evident in "Farpoint" is that humanity/Starfleet was just now impinging on the Q's territory as they expanded farther into space. That idea was later abandoned as subsequent episodes amped up the Q's power to godlike, universe-spanning levels.
The idea that I believe emerged in later episodes starting with "Hide and Q," and which I hinted at in my novel The Buried Age
, is that the Q were testing us because they recognized that we had the potential to evolve to their level.