A common theme throughout the series is Data doing what he could to become more human. But of all the alien species out there, why did he pick human? Why not Ferengi or whatever Q was?
For a start, Data's 'father' N. Soong was human. Children often seek to grow up and become like their parents, and the same instinct may apply to androids created in their maker's image.
Add to that the fact that the majority of the Starfleet officers and other people surrounding Data, the people he might possibly see as role models, were human, and you have a pretty compelling reason why he should see humans as special.
Sure, he might have known and been friends with some non-humans too, but it definitely makes sense that he'd want to be human more than anything else.
In addition to the points made by @rand, there is one other key point: Data was designed to surpass his programming. Considering his programming, the one key thing that distinguishes him from most organic species is his inability to be experience emotions. Yes, he could try to become a Vulcan and with some minor anatomical changes could achieve it, but Vulcans also experience emotions. But what would the point be of working so hard to experience emotions only to suppress them?
The other key point is he was designed in the form of a human, so it is rather logical to aim to become more like them!
I always took Data's attempt to be "human" not literally but more like an image. If you look at the series (all Star Trek series), the human way of life (mortality, compassion, ....) is the dominant factor, and regardless of which species shows them to an even greater extent than humans, it's the humans who are used as the showcase there.
So in essence I never saw Data as attempting to become a human per se, but he wanted traits that humans and other species shared. And due to the series' perspective (and also he himself being designed by a human) he called it to become like humans (the traits being emotions, no immortality, ...).
A common theme throughout the series...
If you take a further step back, I think you'll find that a common theme throughout the series is, "What does it mean to be human?"
The original Star Trek had Spock with a mixture of humanity and something not-quite-human to explore the internal battle, bringing out thoughts, ideas, and concepts on what it means to be human. Rather than trying to show Kirk having an internal battle between what is right and what is just, or what is humane and what is permitted by regulation, this difficulty could be placed on a character who was explicitly designed to make the comparison easier to film and stage as an external exploration, rather than an internal thought process.
While they continued to throw the crew at other cultures and in other situations that would explore their humanity, having a crewmember on board to articulate and compare one perspective - logic, rules, authority - against human perspective - relationships, compassion, justice - makes the exploration easier to exhibit as part of the dialogue and action.
Having Data attempt to become some other species wouldn't have fulfilled that role nearly as neatly, and again you'd be trying to force thoughts and feelings internal to the human crew out into the open.
Notably, some of the other characters served similar purposes. Deanna Troi, for instance, was able to verbalize feelings, important because Data did not have the capability Spock had of exploring human feelings. By breaking the human:logic comparison away from human:non-feeling you can explore more intricate concepts where the two, logic and lack of feeling, are often conflated and difficult to tease apart.