Response: One can refuse to answer questions posed by a grand jury only if the witness can claim a valid privilege as the basis for doing so. The Fifth Amendment privilege against self-incrimination is a constitutional privilege and, as such, can be invoked by a grand jury witness, as long as the requirements for invoking it (i.e., that answering the question would "incriminate" the person, in that the answer would provide the government with evidence it can use to prosecute that person for crimes). The government can deprive someone of their ability to take the 5th if the government gives the person immunity. The premise is that the 5th amendment privilege protects you from having to say things that can be used to convict you of a crime; if the government promises not to use what you say or anything derived from what you say against you (e.g., gives you immunity), then you can be forced to answer because forcing you to do so does not violate what the 5th amendment was intended to protect you from.

Outside the 5th amendment privilege, witnesses can invoke evidentiary privileges (attorney-client privilege, marital privilege, doctor-patient privilege, priest-penitent privilege, etc.) that are recognized in the jurisdiction where the grand jury sits.