Back in 1965, the original Star Trek Captain thought the show was about "man's relationship to woman"

There are almost no interviews out there with Jeffrey Hunter, who played Captain Christopher Pike in the original Star Trek pilot, since he was replaced by William Shatner and then died in 1969 before the show really became a cult phenomenon. But TrekWeb has dug up a 1965 interview which Hunter did with a "Hollywood columnist," which was picked up in Starlog Magazine later. In which Hunter shows a lot of enthusiasm for Trek, as well as some thoughts about how the show might unfold:

We run into pre-historic worlds, contemporary societies and civilizations far more developed than our own. It's a great format because writers have a free hand - they can have us land on a monster infested planet, or deal in human relations involving the large number of people who live in this gigantic ship....

The things that intrigues me the most is that it is actually based on the Rand Corporation's projection of things to come. Except for the fictional characters, it will be like getting a look into the future and some of the predictions will surely come true in our lifetime.

With all the weird surroundings of outer space, the basic underlying theme of the show is a philosophical approach to man's relationship to woman. There are both sexes in the crew and, in fact, the first officer is a woman.

Given how much Hunter's pilot, "The Cage," dealt with Captain Pike's needs as a man and his relationships with his female crewmembers, you can see why he might think that would be a major theme of the show — but Kirk's romances with various alien women notwithstanding, you'd be hard-pressed to argue that gender relations were "the basic underlying theme" of the show as a whole. And of course, the show replaced Number One as Kirk's first officer, giving Spock a major promotion.