I don't want to take anything away from Brythan's answer. It is on point and answers the question. The controversy is easily explained as not allowing the additional witnesses and ultimately not allowing the nomination of Justice Thomas to the supreme court.
However, the answer while on the face of it is accurate, leads to several misunderstandings in context.
First: the hearing is not a trial. While some rules of testimony are similar to trials, they are very different. The hearing is more akin to a job interview. That is, no one is being accused of anything. It is simply, is the candidate politically acceptable to the office he was nominated to.
Second: The role of the committee is to promote the politics of the party in power. In practical terms, it is mostly a rubber stamp to the president's will. I say practical terms because that is what history has shown. The few times that the committee has not approved a nominee it was because the president made mistakes nominating someone who was DOA (Bork for example was already so politically tainted that one wonders what Reagan was thinking) or the president was not as politically savvy as the opposition party. I digress to the point of this paragraph. What is expected is for the committee is to score political points by: embarrassing the opposing party, showing solidarity with their own party, or even individuals demonstrating they are mavericks by doing their own thing. This reads as cynical but ask yourself, does anyone remember who the members of the committee were or the pubic hair on the coke can?
Finally: The expectation of a fair hearing of the victim makes no sense since the hearing is not a trial to determine if Justice Thomas is guilty of a crime. A comment in the answer displays the outrage of Justice Thomas testifying both before and after Ms. Hill. I have no idea where the outrage comes from. If I'm interviewing you for a job and your ex says you are a drunk, isn't it fair for me to call you back in and ask you: Are you a drunk?
Vice President Biden is not the most politically savvy individual but he is in the Major Leagues politically speaking. He definitely weighed the decision of allowing more witnesses and in the end decided that it would not promote the goal. That is the goal of embarrassing the opposition party. I don't know the inner details of his thinking, but it is possible he was right. Recent history has shown that parading additional individuals is likely to backfire.
Contrast what you have now: Ms. Anita Hill, the victim, can be martyred out even almost 20 years after the incident or whenever Justice Thomas does something that is not on the Democrat agenda. Now compare it to what may have been: Additional witnesses that may not pass the media anal exam and have skeletons in their closet and/or are activist. The moment you bring out Ms. Anita Hill, the victim, the opposition can reply with the association of "unclean" witnesses. Take Ms. Christine Ford and her witnesses. If that committee has stopped at Ms. Ford, she would be a victim that could be paraded whenever Justice Kavanaugh is in the news. Now, whenever Ms. Ford is mentioned, the article has to write that the witnesses did not collaborate her story.
The final explanation to the context is why are we talking about this now? Vice President Biden was the Vice President of a 2 term President who remains popular. Vice President Biden announces his intention to run and this story is dug up. It appears that the leadership of his party just wants him to go away.
In response to the comments: I don't think I was clear enough. The argument that Vice President Biden was unfair to Ms. Hill makes no sense. There is no record that the Vice President said anything mean or offensive to Ms. Hill personally. The Nomination hearing is not a discovery of crime nor did then Senator Biden have any law enforcement power to smite Justice Thomas or redress any complaint of Ms. Hill. That is not the right venue for redress or punishment no matter how many witnesses came forward and were listened to. Then Senator Biden was not a judge in the matter of the state vs. Justice Thomas. There is a path for that involving law enforcement and the department of Justice.