I don’t think they necessarily meant anything by it, at least the post that I saw and the people who agreed with it.
It felt like “let’s make this even sadder” rather than any kind of Kara hate. But as sometimes happens with headcanons in this fandom, in an attempt to make things more interesting for them, they compromised the truth of the character.
Really, if you think Kara gave up on that rooftop, you’re sorta missing one of the core messages of the scene. Particularly as conveyed in this moment:
“I’m gonna kill you.”
Kara barely managed to lift her head to look Reign in the eye as she spoke. It was an active, relatively long and painful struggle to do so. And yet her words were defiant.
This was a very purposeful moment to display that—despite being physically incapable of fighting at the moment—Kara was still resisting in the only way she was capable.
People probably read the situation as Kara giving up because she didn’t try to use her heat vision or throw a punch, but she barely manages to just push herself on her knees:
She was even trying to use her weight and balance rather than physical strength to get her torso up straight.
For much of the scene, her head is lolling around:
Trying to actually gauge what sort of physical injuries she had at this point and how they would have logically affected her might be too in-depth for a show that relies heavily on pseudo-science (beyond the concussion they pretty purposefully demonstrated to be the turning point of the battle). But we were meant to see that Kara was only physically capable of moving pretty minimally on her own at the time.
If she couldn’t even keep her head upright on her neck, throwing another punch was pretty much not an option.
Of course, she knew how bad off she was. I don’t think she was necessarily under the impression that she was gonna gain some sudden energy and defeat Reign in a couple minutes, or even that backup was on it’s way.
When she sees the drop she is in store for, knowing Reign’s intentions:
“Welp, that’s gonna suck.”
But the determination never leaves her eyes.
It’s all she can really physically do to fight back, and she takes advantage of it.
And that’s important and purposeful. They made a point of it.
Hell, the remnants of that same determination are still around her eyes as she falls:
And then from that point on I’m pretty sure she’s in la la land—
—because she passes out before hitting the ground:
But the reason the scene is so horrifying to witness is because Kara didn’t give up.
Reign got the upper hand when Kara was distracted by the bystanders, and then she utterly defeated Kara. Kara didn’t hold back, didn’t have the opportunity to win but miss her chance. She was fighting the entire time, as much as she physically could.
She just lost anyway.
The two feelings we’re meant to take away from the scene are the shock and horror of what Reign is capable of and admiration of the fact that Kara never gave in. Downplaying either of those things undercuts the true tension of the scene.
In fact, they highlight Kara’s heroic qualities because it ensures that when she falls, we know what it really means:
Question of Smoke 