This question already has an answer here:
Is it possible for a wizard to research the magical spell within an item, thus learning how it's composed and legally copy it into his/her spellbook?
After some discussion with people who have come with answers stating that it's not possible to learn spells from item which doesn't contain a written spell (like a scroll or a book /tome). I then wonder why it shouldn't be possible for the wizard to research the spell embedded into the magic item, trace the process backwards or just keep using the spell to gain an understanding of how it works and the magics that lies within.
... For a real-world example, it's the difference between finding a recipe, and finding a cake. You can study the cake all you like, but you probably won't be able to bake one exactly like it unless you find the recipe somewhere. ...
This guy definitely has a point, but then again, if you can taste the cake you can figure out what basic components are needed in it, especially if you were a pastry chef or something alike. Shouldn't that go for wizards as well? The reason I'm not satisfied with the given answers is because so far there hasn't been a specific rule stating that it's not possible, just hinting towards and suggesting.
Now if we take the cake example and apply it to the wand, we try to backtrack the process of embedding a spell into a wand. How is that done? Is the spell written inside the wand and thus readable with some kind of divination magic maybe? Is there actually a good rule that helps my case (I want it to be possible, but if I get a solid proof that directly states it's impossible I'm accepting defeat) or is it just up to the DM to make a final decision?
Summary: Can a wizard learn Magic Missile from the item Wand of Magic Missile? If yes/no, why/why not?
After having asked on the official D&D facebook page, I've gotten the answer that it's not possible for a Wizard to learn a spell from a magic item the way I've described it. Here's the direct quotes from the person(s) I was in contact with.
The rules on page 114 of the Player's Handbook are pretty specific as far as to what you can use to copy down a spell. Generally, the rules do not support learning spells from magic items that perform similar roles.
You are, however, more than welcome to work with your Dungeon Master on a house rule for this if you feel like it should function differently!
The rules do only support written sources, as you indicated from that section. Something like a spellbook or a scroll would be able to provide the verbal incantations necessary for a spell, while an item may not necessarily do that.
These are the means that are explicitly provided by the rules. Again, you are more than welcome to coordinate with your DM about a house rule!
We see that the major reason why my theory fell apart (sadly) was due to the wand not being able to provide the "verbal incantations necessary". So we can now all rest as the issue has fully resolved.
The previous question can be found here: From what items can a wizard learn his spells?