The purpose of the episode and many like it, and the whole of Data's character on the show, are to explore this question: is an artificial life form alive? Is it sentient? Is it aware of and responsible for its actions? What is life? What is sentience?
The answer Starfleet gives is... maybe.
TNG tackles this question directly in The Measure Of A Man where Data's sentience, and thus rights as a sentient being, are literally put on trial. The trial concludes by acknowledging that we will never truly know the answer, and thus should be conservative on the point. Picard makes the point elegantly...
"Now tell me, Commander, what is Data?"
"I don't understand."
"What is he?"
"Is he? Are you sure?"
"You see he's met two of your three criteria for sentience, so what
if he meets the third, consciousness, in even the smallest degree?
What is he then? I don't know, do you? (to Riker) Do you?
(to Phillipa) Do you?"
- Picard and Maddox (The Measure Of A Man)
Because Starfleet's role is to seek out life, they take a deliberately conservative view on the subject of sentience to avoid inadvertently stomping on the rights of a sentient creature.
Starfleet is also eager to avoid prejudice, and recognizes that assuming sentience is limited to carbon-base life forms is prejudice. Spock's apocryphal quip that "it's life, but not as we know it" encapsulates that idea.
While there is always doubt and resistance, from Data to The Doctor to the Crystalline Entity, non-biological life forms which act as if they are sentient are given sentient status.
As to whether Data actually cares, the answer to that question is another question. How do you know that humans care? If you can answer that without anthropomorphizing and prejudicing towards meat brains, you will win a Nobel Prize.
Despite Data's own protests, he has certainly acted as if he cares in many situations. Richard's post outlines all the problems Data is weighing as a commander, just like a biological commander would. The difference is that Data is (usually, but not always) self-aware of his complete decision making process and could probably explain it in excruciating detail. Is this significant? Because Data's brain was constructed in a lab rather than grown in a womb does that disqualify him from sentience?
A lot of people would say yes, it does disqualify him, but be unable to give a concrete reason. Often these arguments fall back to stating that Data lacks a "soul", but using other terms. This is exactly the prejudice Starfleet tries to avoid.
Measure Of A Man, and the later Voyger episode Author, Author, discuss the darker side to the arguments against sentience: slavery. Computers, Data, and holograms, were built as servants to do things cheaper, more efficiently and safer than biological sentience life forms can. In Measure Of A Man, Maddox wishes to take Data apart to build more of him. Guinan correctly raises the specter of property and slavery.
"Consider that in the history of many worlds there have always been
disposable creatures. They do the dirty work. They do the work that
no one else wants to do, because it's too difficult or too hazardous.
And an army of Datas, all disposable? You don't have to think about
their welfare; you don't think about how they feel. Whole generations
of disposable people."
"You're talking about slavery."
"I think that's a little harsh."
"I don't think that's a little harsh, I think that's the truth. But that's
a truth that we have obscured behind a... comfortable, easy euphemism.
'Property'. But that's not the issue at all, is it?"
- Guinan and Picard
There is an economic pressure to give servants a lower status in order to morally justify exploiting them. Whether that is social status, racial status, or going as far as to state they lack sentience. Much of the arguments against assigning Data and The Doctor sentience can be traced straight back to the unease at letting go of this cheap form of labor. Author, Author goes so far as to actually show EMH Mark 1 holograms laboring in mines. If you define something as sentient, you can't exploit them without acknowledging that you are now slavers.
That this is beginning to sound an awful lot like a sophomore philosophy class is not a coincidence. Star Trek is intended to tackle philosophical questions. While the series has, often of late and completely in the reboot, lost its way in this regard, it has had its moments. Measure Of A Man was many people's first real challenge to their ideas of what sentience is.
As an aside, there have been cases when Data is unable to explain his likes and dislikes, often stating that "it pleases me". I feel the writers of the show are attempting to imbue Data with a spiritual nature, a soul, and a rich internal life. Data has dreams, he's more like us. Data keeps sentimental items around and cannot explain why, he's more like us. In doing so, they are anthropomorphizing him and making the question of whether he is sentience easier for the audience to handle. I feel this waters down the basic discussion about sentience, that we should be able to accept other cultures and forms of life without the need to make them familiar and comfortable.