Because that's the way it is in actual use? If someone says "Дайте XXX", the assumption is that unless you specify otherwise, you want XXX to be given to you. That's how Russians use it and what every Russian I've talked to would understand. Kind of like in English if someone said "I'll put it in the car" most people would assume they meant their own car unless there was context to indicate otherwise.
I would be very careful about assuming that translations in the course are bad just because it's something you haven't met before, especially if this course is where you've learned the Russian you know. The people who wrote this course speak Russian fluently (and natively), you're only learning it. So if you think the course is wrong, it's best to check with a reputable source - and provide a link to one when claiming it's wrong in the forum.
As a novice who actually wants to learn, please, no matter what they do in Russia, stop leaving out words. I don't realistically know who the spoon is being given to by reading a sentence, nor do I understand the nuances of a language at 180 days into it, on a phone app that I use for 30 minutes a day at best. This is why I gave up on Arabic because the "you'll figure it out as you go" method is annoying. Don't hide/drop words, don't mask/change vowels, don't obfuscate with nuance; pretend I'm a small child in grade/primary school.
You might find it helpful to use the web version (you can do this using the browser on your phone if you don't want to on a computer) and read the tips that go with each skill. If you click the lightbulb icon you'll see them. They explain many of these kinds of things.
Also, sometimes dropping words is done because it's actually required. "To be" isn't dropped in present tense just for the fun of it, but because it simply isn't there in Russian and to try to use it would be wrong. And in something like this, it's really quite logical that the spoon is to be given to me, and it would be a disservice rather than good teaching to not teach that Russians will often leave the pronoun out in this case. It wouldn't be good teaching if it weren't teaching what they do in Russia.
But, small children are immersed in the actual language, with all the real vowel shifts and elisions that everyone uses all the time. So by giving you the actual language with the real vowel shifts and elisions that everyone uses all the time, they actually are trying to treat you the way that small children are treated, no?
I think this is the modern theory of language acquisition, as contrasted with the traditional theory of studying structure.
I myself like the traditional style, like you do apparently, but I am under the impression that the modern style is reputed to give better results.
ло́жка = лОжка = [ˈloʂkə]
That apostrophe risks to be conflated with the IPA sign that indicates stress, and this sign comes BEFORE the stressed syllable.
When ложка is the direct object of a sentence, as happens in this sentence, it changes to accusative case, so the correct form is ложку.
Because it's the direct object of the verb "give" here (the thing that is being given, the thing that "suffers" or undergoes the action "give"), and so stands in the accusative case.
Feminine nouns in -а change to -у in the accusative case.
Also, the accent is not usually written in Russian.
Your sentence requires that both participants are in close proximity. It further assumes the spoon will be handed directly to the speaker. While it is possible that is the case, it is equally possible that it is not. Not every conversation about cutlery takes place at the dinner table.
The Duo translation of the Russian example is not wrong for sure. Quite the opposite. Russians normally use Дайте to mean give me. They may occasionally add Мне for reasons of context but they do not typically do so.
When Russians want to indicate any of your possible alternatives, they make it clear by inserting the correct pronoun. No such pronouns are present in this example.
If a police officer stops you and says.....hand over those keys..., I am sure you do not immediately start wondering who it is that he wants you to hand them to.
I'm not sure why so many beginning Russian language students are so quick to claim Duo is wrong before they even do as little as check out the comments to see what has already been discussed on the topic. It seems worse with the Russian language course than French or German.
ло́жка (lóžka) [ˈloʂkə] f inan (genitive ло́жки, nominative plural ло́жки, genitive plural ло́жек) "spoon; spoonful" From Old East Slavic лъжька (lŭžĭka), from Proto-Slavic *lъžьka, from an earlier *lъga (“bending”) + *-ъka, reanalyzed to have a soft -ž- under the influence of *lъžica. For comparison, consider *vidlъka (“fork”) and *vidlica (“id”).