So i get down to the problem.
I installed Fiddler to see what happened.
My first Problem is, i get from Fiddler a different error as i get from .NET Framework.
Fiddler told me, that the Problem is the verfication of the Server certificate from the server i called.
To verify this, I added the following line of code and tested whether it works:

ServicePointManager.ServerCertificateValidationCallback += (o, c, ch, er) => true;

That worked. That means the problem is that we don't trust the authority's root certificate, or rather, the certificate isn't present in the trusted Root store.

When installing the cert into the root, the problem is solved.

Thanks for the answers.

Edit: For somebody who maybe have the same Problem - Do not use this in prod enviroment.
Just for testcase, but delete it afterwards!