That's where I'm talking about the problem as I don't believe Kara Zor-El should be stuck being the Robin. I've always felt that she should be advancing to becoming the Power Girl (or Superwoman) rather than stuck at being "Superman but half as awesome." That was the premise in the Silver Age because she was meant to be his Mary Marvel. In today's society and certainly on the show, Supergirl is training and fighting and leveling up. Basically, moving from being Supergirl the dorky teen to being Supergirl the Powerhouse like Wonder Woman. The most powerful superheroine in the world and someone who can beat Superman if circumstances go her way.
At no point is Kara Zor El the equal to Robin. She's not a sidekick, never was. He was a mentor to her, but she's on her own, in another city. A student doesn't have to defeat a teacher to be ready. A police officer or a soldier does not have to defeat their instructors in combat to be cops and soldiers on their own.
There's nothing wrong with Superman being more powerful when that's what he's supposed to be. That doesn't take away from Kara and the great work she does. Supergirl SHOULD be a powerhouse like Wonder Woman. But she shouldn't need to fight Wonder Woman to do so.
It showed major insecurity on the part of the writers for them to not only have Kara win that fight, but to have Superman constantly spewing how Kara was better than him--in multiple appearances.
As for Superman, I tend to prefer Animated Series Superman to Silver Age Science God. A guy who is really powerful but under the right circumstances can be punched out by Zod, Doomsday, Darkseid, Lobo, Kalibak, or sufficiently strong Kryptonian Battlesuit Luthor. It justifies the existence of the Justice League that there are threats you need backup for Superman against. Now Superman will win the vast majority of these fights but not so much that Zod can't beat him in the first act only for Superman to rally back.
That's not how Zod would beat Superman. Look at Superman II for example. Superman took on 3 Kryptonians and gave as good as he got, but even so, he lost the first battle--not because he was overpowered, but because circumstances put too many people in danger. He had to flee not because he was physically beaten, but because he needed to take the fight to a different location. Yeah, there are villains who can hurt him, but in the end, he wins--he's Superman.
So yeah, if Superman is invincible against anyone save Darkseid (who is the Space Devil and a league of his own) then obviously Supergirl beating him is a bad thing. However, if Supergirl is meant to be not Robin but evolved into Super Family Nightwing then I think that's okay. Because while Batman would probably win usually against Nightwing, I can see Nightwing beating Bruce--especially in his own comic/show.
I think that actually makes Nightwing look weaker--for the same thing. One doesn't need to be the most powerful to be a hero of equal stature. Batman is more experienced and better trained--he SHOULD be able to beat Nightwing. But heart, determination and sacrifice are what makes a hero.
Think Dan Turpin in Apokolips Now. Was he any less a hero than Superman in that story? In some ways, he was even more of a hero because he did that with no powers.
Same with Steve Trevor in Wonder Woman--what a difference? The writers of that movie were secure enough in Wonder Woman that they didn't need to make Trevor look weak. He was a hero in his own right, and so was Wonder Woman.
And as I've pointed out multiple times before, it's logical that she could outfight Superman regardless of their absolute strength levels, because she's had military-grade combat training from Alex Danvers, a woman who routinely outfights men bigger and stronger than herself, whereas Superman is a self-taught brawler. Technique is more important than raw muscle.
Let's not overstate a few months of lessons with Alex. And let's also not forget that this version of Superman went to Warworld and if that story followed through, he would have beaten Mongul, who could destroy Alex Danvers. Superman is more than a self taught brawler. This is a Superman that has known Batman in his universe. Chances are Wonder Woman is part of that universe as well. He would have trained with both of them, and both of them were far superior.
Also, unless you are completely untrained, size matters. Maybe in TV, Alex Danvers could hold her own, but you stick Ronda Rousey against a trained fighter that outweighs her by 50 pounds, she will get crushed. A trained big person will always beat a trained smaller person. That's why weight divisions exist in the first place.