I'd be interested to know what subjects the professors making these arguments teach, because from a historian's perspective we can never really know. She did not leave a secret diary entry or letter that speaks to us candidly about the subject, so we can only talk about what is more/most likely to have happened.

Certainly her virginity was important politically. On the basic level, she was a high-status, unmarried woman, and for that group, sex was off the table. Of course, for the vast majority of unmarried aristocratic or royal woman, this is because they were young and preparing to be married; in a patriarchal culture that saw female premarital sex as an indicator of future sexual misbehavior, it could ruin their reputations and make them unmarriageable. As long as she was entertaining offers from foreign princes, there could be no public speculation or rumor that she was "unchaste" or else the offers would stop and her people would become incredibly hostile toward her.

By the time she was 40, it was clear that she didn't intend to get married, but her virginity was still useful. It set her apart from married queens like Mary Tudor, Jane Grey, and Mary Stuart - queens who, from her and her partisans' perspective, were also flawed and not the rightful heirs to the kingdom - and made her symbolically pure and incorruptible. When it comes to literature and poetry, I'm not the one to talk to, but basically: her status as a virgin was used to compare her to mythological and historic figures.

People largely theorize about Elizabeth not being a virgin in relation to her feelings for Robert Dudley, a close friend she romantically loved and seriously considered marrying after the death of his wife - a death that he was rumored to have caused in order to marry the queen; after he married someone else, she reacted with what was almost definitely jealousy. If she had been going to risk her reputation and possibly even her throne, it would have been for him.

Ultimately, we can't know, as I said before. However, the absence of evidence points toward her not doing that: she would have been surrounded by servants, pages, guards, and ladies of the bedchamber at all times (as your professor said), and if she had done something sexual in front of them or dismissed them all in order to meet with Dudley in private, it's unlikely that they all would have taken it to their graves. That there was never a scandal or an allegation of sexual misbehavior despite the many people who would have had to work to conceal it implies that it probably didn't happen.

But ultimately ultimately, it doesn't really matter. The contemporary obsession with the question (which didn't seem to bother nineteenth-century folks) has little to do with the logistics of the issue, and more to do with a) a prurient desire to dig through a powerful woman's sexual history to find that she lied about it, and/or b) a disbelief that an adult could go without sex for life or could divorce romantic and sexual feelings. While it's clear from historic legal cases involving premarital or extramarital relations that unsanctioned sex has always been of interest to people despite the fact that it was frowned upon, we live in a fundamentally different cultural landscape. We no longer have much interest in unconsummated love and devotion from afar, unless perhaps it's unrequited and never admitted publicly, so we think that if two people loved one another they must have tried their damnedest to find a way to have sex.