I will leave you this quote from a famous lawyer.
“The defendant wants to hide the truth because he's generally guilty. The defense attorney's job is to make sure the jury does not arrive at that truth."
The way he said it in class is that: As a prosecutor your job is to make the truth come out; as a defense attorney your job is to prevent that from happening. He also said, that a defense attorney's job is to get guilty people off.
The prob in this case is that the prosecutor is not just trying to get the truth out--they are acting as advocates to put him in prison regardless of the truth. That is how they prosecuted even though there is no way they possibly believe themselves beyond reasonable doubt (which is a requirement to prosecute). That is the explanation for the bizarre objections to reasonable requests and things from the defense.
It isn't supposed to be like a civil case where each side just wants to win. The prosecutor is supposed to just want the truth to come out--whichever way that is.