Of course in Halo humans may not have beaten the Covenant if it weren't for the civil war and the elites joining forces with the humans. Humans had consistently gotten their ass kicked by Covenant repeatedly, aside from some small victories by Spartans.
We never felt those losses though.
Sure the background lore was that the Covenant were winning, but you routinely have Spartans or even regular four person ODST squads laying waste to entire armies by themselves on the ground, while severely outclassed ships were forcing defeat, or phyricc victories at worst, out of the advanced alien fleets. There never was any fear for the fate of humanity because we would routinely defeat the forces of the Covenant, Flood and Forerunners with our sheer tenacity and human ingenuity. The Elites aid us, but that is a mere footnote in the narrative and we have yet to see more of the Arbiter or other friendly Elites outside of bit cameo appearances.
Mass Effect is probably a little different in this regard since humans start off as having some semblance of parity with the council races by the start of ME1, at least with respect to their economic and military strength if not in representation and respect. I thought they did an ok job with the idea that the Council tries to play humanity against some of the other races. They have a seemingly never-ending series of hoops for humanity to jump through, like using the Alliance to expand Council influence in the Attican Traverse, along with the promise that after the prove themselves Humanity can join the Council.
But humanity never feels like the underdog in these scenarios. Oh no the Council doesn't respect us, and yet we have an embassy on the Citadel, with our ambassador having his own separate office no less, while the Volus and Elcor; two species that have been apart of Council Space long before humanity has; still have to share a room and have no prospects of making it onto the Council itself.
This becomes even more ridiculous in ME 2 & 3 where you have a human Councilor, and human workforces filling up almost all of the positions of authority on the Citadel, and yet you have groups like Cerberus going on about human dominance and looking out for our species. We're already on the top of the pile, quite the opposite of being the underdog.
I felt that the Hanar, Elcor, and Rachni would have been better candidates for that moniker than humanity ever was throughout the ME trilogy.