Why Elizabeth never married

It's much more complicated than that.

There are a lot of indications that despite the opposite being believed, Elizabeth did want to marry her whole life if it was about her wishes only, all the way up until the potential French match in the 1570s that she was serious about herself. But other political considerations made it impossible. Parliament and the British people hated the French and the idea of her marrying any Catholic.

Like her sister, Henry's constant policy changes and changing alliances kept delaying potential marriage while she was a young woman when most are married. Then of course no way that she was getting married while her sister was Queen since she would insist that Elizabeth marry a Catholic and be sent away. So she's 25 when she takes over and still plenty of people who consider her illegitimate due to Catherine being alive and Henry not being married in the eyes of the Catholic church, so she had to be extremely careful and the right suitor never came along at the right time. It was just too big a risk.

One must certainly imagine that besides what happened to her mother, looking at what happened to Mary, Queen of Scots and how she was utterly ruined by the men she chose as her husband's had to play a big role in it.

But one can't help but think that in terms of the monarchy, it was terrible for the long-term. Henry would have been furious with her for not marrying. Not 50 years after her death a British King was put to death by Parliament and only 100 years later, the Germans would take over the throne under the conditions that Parliament set and of course they lost more and more power until it was only a ceremonial position.

If Dudley's wife had not died the way she did, then it's very possible she would have married him, whatever Cecil and her advisors wanted. An English Protestant wouldn't turn Parliament and the people against her like say an alliance with a foreign Catholic.