I think you misunderstand. The goal of the game is to convince everyone you are one of the progressives, and not an informed extremist. As long as you are proven to be progressive, people should be able to rest assured that there are no falsehoods in your statements and you can be trusted to push progressive policies forward.
And your other main goal as a progressive is to determine who your allies are. Knowing whose word can be trusted is the key to pushing progressive policies and victory. Right now @DaBackpack and @Yerian are the most trustworthy, and you and @Rabla are the least.
The only benefit a progressive might have for withholding information is if they are trying to manipulate the extremists. But any attempts made to hide the truth will be seen as strong evidence that you are an extremist and have something to hide.