Why does Baron Zemo think super soldiers cannot be allowed to exist?
Remember what Vision said on the issue in Civil War?
In the eight years since Mr. Stark announced himself as Iron Man, the number of known Enhanced persons has grown exponentially and, during the same period, the number of potentially world-ending events has risen at a commensurate rate… Our very strength invites challenge. Challenge incites conflict and conflict… breeds catastrophe.
This is essentially what Zemo was fighting against.
And if you want it from the horse’s mouth, this is what he said:
The desire to become a superhuman cannot be separated from supremacist ideals. Anyone with that Serum is inherently on that path. [Karli] will not stop, [Karli] will escalate until you kill her. Or she kills you.
And if you need any further confirmation on the matter, look no further than what Dr. Erskine himself had to say about it:
The serum amplifies everything that is inside. So, good becomes great. Bad becomes worse.
So, why does Baron Zemo believe that super soldiers shouldn’t exist?
It’s because they’re human beings with superhuman abilities. You can’t blindly trust that they wouldn’t abuse their power for whatever goal or desire they see fit to achieve.
Human beings are possibly the most easily corruptible species on Earth. The Avengers were by definition superhuman and, while they did protect the Earth from several world-ending threats, they all needed to take responsibility for whatever things happened under their watch.
When Bucky turns it around (extremely validly) and says that the Serum never corrupted Steve, Zemo agrees, but turns that notion on its head and rhetorically questions “But, there’s never been another Steve Rogers, has there?”
Steve Rogers was an exception. He proved from his first appearance that he was a paragon of virtue, always standing right back up to do the right thing, even if it cost him his life.
Just because he inspired others to follow his example doesn’t mean that other people would possess that same quality.
And, if by divine intervention, Zemo is proven right with this exhibition:
A superhuman like Steve would never have given in to his base senses and cold-bloodedly murder a man in broad daylight, no matter how severe his past transgressions.
But a man like John Walker would, because he’s human.
Not to mention his personal stake in this; Zemo’s family was killed during the midst of a battle between a murderous super-bot and a group of superhumans.
If you were him, why wouldn’t you believe they shouldn’t exist?