There really wasn't just one specific reason but the broader reason is generally held to be to maintain her personal sovereignty and security. Which is a bit more complicated than "didn't want to share power."

To start off very broadly, Elizabeth was by nature an extremely cautious person. In every sense. When it came to foreign diplomacy, war, money (especially money), and political appointments. Sometimes that cautiousness lead to indecisiveness, which drove her council mad. So by her very nature a huge decision like marriage was never going to be one she took on lightly.

A primary concern of her's was that during this period a man was expected to dominate over his wife. A woman's property was expected to be turned over to her husband upon marriage. So, regardless of what title he had, any man she married would be expected to at the least exert a lot of influence and at the extreme become king of England, himself. This wasn't a hypothetical concern. Phillip's exact role during the reign of Mary I was a continuing problem. Contrary to perception, Mary, despite being very enamored of Phillip, was firm in her own sovereignty (Mary was as much a Tudor as her father and sister.) Phillip was titled king but he couldn't act without her consent or appoint minsters. Phillip was not pleased with the arrangement, which lead to tension in the marriage. And many blamed Mary's desire to please her husband with being involved in a war against France that eventually lost Calais. Although the loss of Calais was probably a good thing in the long run, it was seen as a disaster. And her marriage was not popular. So that example was certainly on her mind.

Elizabeth would want to avoid such a situation. So, choosing a husband was a very tricky matter from the outset. If she chose a foreign prince there would be endless negotiating over the terms. As there was in her many marriage negotiations. Marrying a subject may have been entertained but it was really a non-starter. Elevation of one subject above all others was a sure way to exacerbate factionalism (which was a problem in her reign.) This is even true when a king did it (Henry VIII's marriages within the realm did see the rise, and then sometimes fall, of the families connected to his wives and adjacent factional conflict.) But with a Queen it was a far greater issue because of what I discussed above about a man dominating his wife.

Religion was an issue. It's not as though there were no possible protestant matches. She and Eric of Sweden negotiated a possible marriage for a very long time. But marrying a Catholic wasn't necessarily an insurmountable problem. Elizabeth also had very serious marriage negotiations with the Archduke Charles of Austria that lasted years. In those it was promised he could have his own chapel for worship. Although it was definitely a concern and the more staunchly protestant subjects would have issues with it.

Elizabeth's final marriage negotiation was with Francis Duke of Anjou. And she seemed to take that very seriously. In the end, it was actually Parliament that urged her not to marry him and she was reportedly livid (although this could have been a form of theater for her it's always difficult to tell with Elizabeth.) She was in her 40s at this point. And even if she could have a child it would be very dangerous. The fear of losing the Queen in favor of an infant with a French royal father was too great. There was also objections over his religion. The strict Protestant faction grew over the course of her reign (although not with her encouragement.)

As talk of those negotiations suggests, it shouldn't be thought that in 1558 Elizabeth decided not to marry and then stuck with it. She considered various matches very seriously.

There was another benefit to her being single. She was able to play the marriage game for the first few decades of her reign. Marrying into England was a very valuable prize to dangle in front of a prince. Elizabeth was very concerned about the prospect of Catholic powers allying against Protestant England. But for as long as she could suggest a possible alliance with one or the other she was able to prolong peace. Her most serious negotiations were with Charles of Austria, who like Phillip II was a Hapsburg, and the two successive Dukes of Anjou (Henri then Francis) both sons of Henri II of France and Catherine de'Medici. This was very effective in maintaining peace, which was very important to her. And with the exception of small expeditions she reluctantly allowed in the Netherlands and the revolts in Ireland starting in the early 1580s, Elizabeth did keep England at peace for roughly 29 years. She ended Mary's war with France in 1559 and the Spanish Armada set sail in 1588.

Had she married into France or the Hapsburgs she could have been sucked into war much sooner. Had she married into Sweden her hand in marriage couldn't have been used as an alliance tool. Had she married a subject it would have brought her very little political gain at all.

Elizabeth was also very aware of the potential for rival courts to form around named successors. This had happened with her while her sister Mary was still alive. A husband and, especially, a son could be direct competition. (And Mary Queen of Scots did have this issue with her husband.)

The lack of succession plan certainly made people of her time very uncomfortable and uncertain. And it added a needless uncertainty when it almost every other area Elizabeth preferred stability over all else. Parliament urged her to marry in the first half of her reign and then urged her to name a successor in the later half. It can be glossed over in retrospect because the succession was very smooth. But it might not have been had she died sooner. So, it shouldn't be dismissed as a very valid concern through out her reign.

But, from Elizabeth's POV, the immediate problems that came with a potential marriage overshadowed the long-term issues of not producing an heir. Elizabeth ruled for 44 years. And her motives and the needs of her country changed over that time. Although she expressed her desire to remain single very early on, it wasn't just a random choice not to marry that she stubbornly stuck to. Really, she never found someone where the positives outweighed the risks. Or if she did ever find the right person it was Francis Duke of Anjou but her council and Parliament were opposed by then.

ETA: I do hope this answered your question. There isn't a consensus on one very narrow answer. Because there were a few reasons and things changed over time. But, ultimately, it was about the security of her sovereignty.