And that's all well and good. I think it's safe to say that fans generally accepted this arc at face value, that it was perfectly fine for him to have this goal, as it helped him be the classic Spock figure in the franchise, commenting on the human condition from an outsider's perspective. But really, why would an android want something like that? I mean, especially for an organization like Starfleet, Data would have every advantage over his colleagues. Although maybe that's the point.
Data was created by the eccentric scientist Noonian Soong, who had been driven to the fringes of society in the pursuit of his dream. The initial results of Soong's efforts perhaps justified this position, the terror of Data's complete opposite, Lore, who in fact called up the destruction of the colony world where Soong worked by communicating with the Crystalline Entity, among other bad behavior. Soong was so scandalized by this prototype who acted too human that he started from scratch when he began work on Data.
Years later, Data was discovered in the ruins of the colony by a Starfleet survey mission, and appears to have made the decision on the spot to join the organization. He advanced through the ranks in the common way, acting like just another recruit and then serving on various starships as just another member of the crew. The only captain he ever had who seemed to recognize that Data was special was Jean-Luc Picard. And it appears that under Picard's command Data felt most free to pursue his passion of becoming more human.
But again, why would he want that? Chances are, because of a culture of fear. He probably didn't encounter too many humans who accepted an android being an android at face value. Although robotic life was present as far as Kirk's time some seventy years earlier, it was still the exception to the rule. Like Spock (the only regular Vulcan), like Worf (the only Klingon), and later Nog (the only Ferengi), Data was one of a kind, the only artificial being to serve in Starfleet.
It's far easier to accommodate inclusiveness when there are a lot of individuals being assimilated into a culture, when you don't feel you're making a special effort because you see many colleagues you know making it, too. It's far harder when it appears to be very much the exception.
Data being Data, who at the time of his rescue didn't have emotions, he probably didn't register hostility against him as anything other than observations. But all the talent and ability in the world can't be used properly when it isn't encouraged to reach its full potential. Then again, maybe Data scared Starfleet, made it feel as if the whole concept might become obsolete if you had a single individual who could perform the same functions as an entire crew complement.
So instead of using his vast computing capabilities to their fullest extent, Data goes with the flow and more or less lives inside his own head for years on end.
And, eventually, decides that someone who can do anything only wants to be more human. Perhaps it's a response to a feeling of being excluded, always being left out when he can't understand how his colleagues seem to get along so well with each other.
It may also have started as an experiment, a challenge Data took because he saw it as a challenge he couldn't easily meet, something that would be incredibly rare for him. We'll call that the positive alternative in this discussion, and it's a perfectly valid argument. At some point, it would have become an obsession, so that he no longer consciously remembered in that neural net of his the original impetus.
But you have to admit, Starfleet has a poor record in his regard. Even after years of distinguished service, Data is still considered an object rather than an individual. Picard has to defend his valued officer's very existence in an impromptu trial. And in the years to come, the Emergency Medical Hologram program proves that if the debate is shifted to a different lifeform than Data, the results of this victory on Data's behalf are easily nullified.
Perhaps the fear is warranted. There's the Borg to consider, a collective of organic individuals who have decided (through coercion) that machinery is needed in the equation to perfect it, reach perfection itself. In a way a purely artificial existence is the end goal of the Borg mentality, a gradual retroconversion process that doesn't hesitate, much as Lore behaved, to ignore the massive harm it causes along the way to achieve it. Cold logic, in a twisted way Vulcans would never approve.
The idea of a robotic lead character was something that fascinated Gene Roddenberry for years. It might be argued that Data was based on the earlier Roddenberry creation Questor, star of an aborted 1970s TV show. Star Trek's creator also had the conflict between artificial and human life on the brain when he conceived Star Trek: The Motion Picture, which many still believe offers an origin for the Borg in the machine world V'ger comes back from to start its insane quest to meet its own creator, which it subsequently refuses to believe could have been something other than a direct reflection of itself, a man rather than machine.
A good episode to explore some of the implications of Data's quest would actually be "Deja Q," in which the merry prankster Q is made human as punishment for his mayhem, and ends up bonding with Data during the transition process, an understated if elegant commentary on the whole affair. Why would Q, who had never previously nor again bother too much with Data, spend so much time with the android in the one circumstance where he seemed least fit to offer guidance? Because they were in the same boat. Data wanted to be human. Q was forced to be human. Both of them tried to figure out what these circumstances mean. And so they learned from each other.
We meet another of Data's "brothers" in Nemesis, the prototype B4, who is a child compared to Data and Lore, sporting only basic cognitive abilities. It's almost an insult to consider that Soong could have created something like him, a huge step down from his siblings. Was he an earlier effort, or perhaps later? Either way, Data takes it upon himself to give B4 the chance to grow beyond his original programming as well, downloading a complete set of his memory engrams into his brother in an effort to spur development by way of increased curiosity.
Was that it, though, was it mere curiosity that caused Data's quest in the first place? I know I suggested it already, but could it have been something so cold as that? It seems unlikely, at least in later years. His friendship with Geordi La Forge was genuine, that much was apparent, perhaps because Geordi didn't judge him (because he himself knew what it was to be an outsider), and could actively help in mechanical matters, even when he didn't agree with the end results (such as all circumstances around the emotion chip that dominated Data's later development).
Data was a product of his creation, but he was also the son of the environment around him. Regardless of Starfleet prejudice, he appears to have been motivated by the need to adapt himself, to be something more than he was when he started. Tellingly, every step of the way he never stopped being himself. He always remained true to his unique perspective, no matter how much he studied the world around him. Did Soong construct a dreamer? It appears so. Data's only ambition was to explore the possibilities of the universe, and humans were a way to appreciate them more fully. So in the equation of his life, Data computed that the best way to achieve his goals was to become "a real boy."
Did he take himself for granted, along with everyone else but Picard and his crew? Perhaps. But for Data, I don't think this was cause for too much concern. He created android life, too. He knew what that was all about. He didn't see himself as a set of incredible abilities, but rather the abilities he was lacking. If nothing else, that's the Star Trek message in sum.