The 5th Amendment privilege doesn’t work the same way in front of Congress as it does in a courtroom.
The basic idea, and this applies to all sorts of privileges, is that you can’t just use a privilege to keep quiet about stuff that makes you look bad, while being willing to ignore the privilege and answer when it’ll make you look good. So if you have a privilege, divulging some privileged matter will waive it (or at least, will waive it w/r/t every question about that subject). Ergo, if you want to invoke your privilege at all, you have to use it to somethng like the fullest extent possible.
During the HUAC period, it was considered that answering any question would waive the privilege. I don’t know exactly the history of that legal doctrine, but it’s what had been established. So it’s not that this guy is being obstinate. It’s that he has a constitutional right not to testify, and the way the law is structured, he must engage that right fully – if he gives any answer, he (at least arguably) loses his ability to object to any question.
–Cliffy