There is actually a lot of speculation about this but the most predominant answer I have seen is that she knew it were undermine her ruling authority. There are further theories out there involving the Spanish, or psychoanalytic writings about her relationship with her sister Mary or father but that entirely depends on how much validity a person places on psychoanalysis as a tool to interpret history.

As a queen and a woman, in the given time period it was expected that she would marry; the man would then assume certain responsibilities that were thought could only be done by men (such as warfare). Elizabeth was incredibly intelligent and knew that no one could force her to marry (as she held supreme dominion as monarch) and that she could hold off the social pressure of the public by appearing to be courting suitors.

This is a very complex issue, and to be honest, there's not a 100% certain answer that explains everything. There are several factors that are generally accepted as reasons, but the weight of each factor is undetermined and can only be considered a factor and not necessarily a reason.

A Woman Ruling in Her Own Right

Prior to Elizabeth (I'll just refer to her as "E" going forward), there had only been one woman who had ruled in her own right; that was E's sister, Mary I. Prior to Mary I, the ruling monarch had always been a male. The queen was the king's consort. We tend to think of the queen as an assistant ruler of sorts, but this was not the case. Although the queen could plead for a cause or interact with ambassadors, she had no real power. She was the king's spouse, and that's that. To be blunt, the queen was the woman chosen to bear the king's children; that was her one and only role in life. That's why royal marriages were made based on alliance opportunities and family lines.

In English history, every attempt at a woman holding some sort of power had failed. Matilda was run out of London after defeating Stephen's army because a woman would not be accepted as monarch. Isabella was called a she-wolf after leading the deposition of her husband, Edward II.

Mary I was the first woman to rule in her own right as monarch after her half-brother, Edward VI, died. There were all sorts of unknowns. Chief among them was the question of marriage. Would the queen's husband be a consort in the same way as the queen had always been to the king? Or, because it was a male-dominated world, would the husband assume power and rule as king, relegating Mary I to the role of consort? Additionally, because the marriage would be to a prince from another realm, there was the additional question of whether or not that male's kingdom would inherit the English throne.

So, Mary I screwed up by marrying Phillip of Spain. Elizabeth would not make the same mistake. She saw how many uncertainties crept up from Mary's matrimonial decisions, and she was determined not to make those same mistakes.

Religious Turmoil

After Henry VIII broke from Rome and created the Church of England, the country was divided. In the decades that had followed, Protestantism had grown, and Catholicism had declined. However, there were enough devout followers on each side to make trouble for everyone. Henry VIII's successor, Edward VI, was devoutly Protestant; his successor, Mary I, was just as devoutly Catholic. These two monarchs had increased the religious tensions in the country.

When E came to the throne, she had to face the question of religious conflict and marriage. The big powers of Europe were devoutly Catholic in their faith. E, however, being Protestant, would be looking to marry another Protestant if she ever decided to marry. No matter the decision she made, religious tensions would only be heightened. So, the decision remain unwed was the best possible choice to prevent further turmoil.

I am having a bit of a problem with several points made in this answer though I am in general agreement that Elizabeth did not marry to maintain her authority. It is also difficult within the context of her Europe to find a Protestant lord who would have been a suitable match for Elizabeth. First when Mary Queen of Scots married Henry Stuart Lord Darnley he was only named King Consort so a recent precedent did exist for Elizabeth to marry and continue to be the real ruler. True, Mary's example was not very positive. Second there was very real pressure on Elizabeth to marry and bear an heir. This was a imperative in monarchical Europe. Andrew Hadfield in his biography of Edmund Spenser argues Spenser criticized Elizabeth for exactly this, albeit metaphorically. Third, I do not quite understand what some commentators mean by Elizabeth "settled" the religious issue. Edmund Campion would not agree. Furthermore, the entire English civil war was fought over religious issues. I think it would be more accurate to argue that William's coup against James the second who wanted to make Catholicism the state religion settled the issue. One historian I read and I apologize since I cannot remember who argued that the Glorious Revolution showed a monarch could no longer change English religion by whim. Finally I am disappointed no Redditors mentioned Ben Jonson's nasty rumor suggesting Elizabeth was sexually abnormal (perhaps a hermaphrodite) nor Mary Queen of Scots scurrilous letter written from her captivity accusing Elizabeth of prowling her castle halls looking for illicit sexual pleasure. This is Reddit!

How did it work out in the reign of William and Mary?

As I remember it was Mary who was the heir.

Who actually exercised the royal power?

It would not only undernine her authority if she married (because England had a terrible track record with fenale monarchs) but thebprospect of marrying the leader of a reasonably prominent European Kingdom like England really enabled her when she was making political deals.