I was wondering if there was an explanation for why Data from ST:TNG couldn't use contractions?
Prior to the 12th episode of the series, Datalore, Data did use contractions. In Datalore, his tendency not to use them was pointed out by Lore:
However, at the end of the episode, Picard asks:
And Data replies:
After this (fairly early) episode, Data rarely used contractions again (so it was somewhat of a retcon). In the cases where he does, it's generally because he's playing another character (e.g. on the holodeck), or to demonstrate an enhancement to his original programming. For example, in Insurrection, after he has received his emotion chip, he says to a child:
So Data could, in fact, use contractions, but generally did not. The suggestion is that his original programming did not provide enough information to use them spontaneously in everyday speech. Perhaps also, given that Lore had mastered contractions, this was a deliberate limitation in Data by Dr. Soong, like excluding emotions, to make the android more acceptable to others. (And one that, like emotions, was intended to be overcome once Data was older).
Lal, the android Data created in The Offspring, did master contractions:
More information, and in particular more examples of when he does use contractions, on Memory Alpha's page on Data.
I'd like to point out a possible alternative explanation, although I do not believe it to be official canon: English is hard.
Data had to learn how to do almost everything. While he almost certainly had basic English programmed into him, I find it more likely that contractions weren't necessarily programmed in, beyond (possible) the most common ones. The rest, he's had to actually learn, and is having difficulty with.
One reallife example is human children and English conjugations (This is an exaggerated/paraphrased example; I couldn't find the article I read this in):
The "forgetting" is because instead of just repeating the phrase by rote, they're trying to figure out why it's "want" instead of "wants". It's a step towards ingraining the rules of grammar so that it's automatic.
I believe that throughout TNG, Data is somewhere between points 1 and 2. Soong had programmed in several contractions for Data to make use of, automatically replacing words with their contractions if he was going to say them aloud. Data had, by the time of TNG, been unconsciously replacing some of those protocols with the more formal form, in an attempt to learn the patterns involved so that they could be applied more generally.
Point 1 is supported in that Data's contractions are often either some common phrase ("I'm fine."), repeating something someone else just said (where he doesn't have to figure out anything), or manually programmed into himself ("Honey, I'm home!").
Point 2 is supported by Data's use of the formal form becoming more common as the series progressed. After Lal pointed it out to him, it could even have become more ingrained, something he was doing unconsciously to be more unique. (Part of what drove Data was to become more human, and one of the key qualities about humans is that we're all different from each other, while machines are not)
Point 3 is supported in the series finale of TNG, in the timeline where Picard is in the future - Data can fully use contractions in everyday speech.
I am not a native speaker of the English language, and as such, speak with what would be considered a heavy foreign accent. I believe my condition can explain Data's. I can imitate the US accent pretty well, and have had native speakers praise me on occasion. But, I can only do this while doing something relatively trivial, such as engaging in social conversation (small talk). When doing something mentally taxing, such as teaching physics, I have to revert back to my heavy foreign accent, because I just do not have the mental capacity (literally, processing power) to mentally translate each sound in time for normal speed speech, as well as perform whatever intricate computation I am required to on the board and in my mind.
Believe me, regardless of how closely and correctly I try to match a mode of speech not natural to me, and how well I succeed, it will always be a taxing computation.
And, oh yes, while teaching physics, I drop contractions!
There's an instance I haven't seen on ANY comprehensive list of Data's "contraction slip-ups", in season 6 ep 21 "Frame of Mind" around 27 seconds into the episode where Data says, "You mean you don't think you should stand trial..."
This contraction really got me thinking, since it's not a sentence Data's coming up with on his own. It's a line in a script he's reading. Any thoughts on how his brain would work? Obviously he can memorize a string of sounds and repeat it, even if those sounds are contractions. But if he can master THAT, why can't he use contractions as parts of common whole phrases?
Though many aspects around this is covered by other answers it is also worth mentioning that the Writers Guide specifically mention that Data uses a more formal version of English then the rest of the crew. Directly quoted:
This support the fact that he can use contractions, but usually avoids it.
Of course, as the Writers Guide was written before the series started, the aspect of this fact get more complex as the universe grows. Another detail about Data's nature is described further in the guide by:
This is one of the reasons, I believe, we see the language Data have. A central part of being human is language. Further one thing that is special and that require more then pure linguistic skills are for example the use of idioms. Understanding language beyond the pure glossary and grammar is one of his quests.
One early encounter on idiomatic expressions is when Riker asks Data do do a data search.
Data is in many ways shown to be like a highly educated / having a vast memory bank as well as mastering languages etc. but very often it also comes forth as cold facts and very correct. When it comes to language specifically it is formal by which this correctness is mirrored.
The formal language is believably also a consequence of Data being set to hold and communicate facts. The formality given is something you also expect in for example a lexicon, a formal letter or other text. One would not expect to read: "Adolse was king of Nagaria for twenty years and ruled it with an iron fist. As a party animal it was only fit he kicked the bucket one fatal night whilst painting the town red."
All of this also makes the use of contractions, as in lack there of, part of what one expect.
Some of the other answers describe the problem, but not the reason.
tl,dr: Data was nerfed to make him more appealing to humans. Humor, emotion and this minor language problem, possibly his love for humans was a trick too.
Data's twin homebro, Lore, is pretty much identical to Data. The thing is that he's a robot which is better than humans in every way. That made him pretty arrogant (he is made to be human, emotions included), and that made him disregard humans.
That and probably his tendency to lie, trick, make fun of people and demonstrate his superiority made the settlers on the colony he was made (by doctor Suung, genius outcast professor) pretty fucking worried. They really kinda just wanted Suung to turn the thing off.
Soong was sad, of course, but Lore contacted the "Cristalline entity" through kind of vague means. Of course that entity was far superior to humans (Source: Lore). Coincidentally it feeds off the lifeforce of humans, entire planets at the time if it can. It was also really fast, like warp fast. Cool thing. Offtopic more here.
Lore contact the entity before he was disassembled. Soong made his second robot with deliberately impaired features like his emotional response, as to not frighten the settlers. See also the uncanny valley, on why that might've helped. Seemingly Soon also fixed the extreme evilness that Lore had, possibly through introducing obedience or admiration of humans. Which would explain Data's goal of having the human experience.
So: Data was made not to use contractions by Soong, possible just as an unimportant gimmick to make humans like him more. Along with other pinches in his capacities elsewhere, like his understanding of sarcasm, inability to laugh, etc.
It was shown that Lore and Data have the same capacities other than in those areas where Data was "pinched". I guess Data is better as he's not adversarial and delusional, although it makes him illogical in many ways. The superiority discussion, of course, could be done later. One also wonders why there's only two prototypes, given Soong still lives.
But hey, that's Star Trek. It works 3 steps of thought more than almost anything else, tells you something about yourself and society without talking about you, and gives you hope for humanity. But a step more the seams start to crack. Why isn't the teleporter all powerfull? Why isn't a superhumancomputerhybrid king of the universe (they actually did that one), etc. Offtopic again. Sorry again. I'm going to stop talking now.
As a programmer, I can semi-humorously say that it just could be an "oops". After all, one guy designed and programmed Data. I'm sure that "English contractions" were way down at the bottom of his list of things to code.