The skeleton description says that while it cannot speak it, it can understand the languages it knew in life. Can it not speak because of its undeath or could it learn to speak a language?
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If it was physically capable of speaking, it would be able to speak the languages it knew in life. It still retains its knowledge of them, so *knowing* how to speak a language is not the problem. The problem is that a skeleton lacks lips, a tongue, vocal cords, a voicebox, and lungs. Speaking is simply impossible.

The Monster Manual entry on skeletons says:

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> They can't read, speak, emote, or communicate in any way except to nod, shake their heads, or point.
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> 
> 

From this, it seems clear that it is meant to be impossible for skeletons to communicate in **any** way other than the given nodding, shaking, and pointing.
It is true, on pg 272 of the 5e Monster Manual, it states:

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> They can't read, speak, emote, or communicate in any way except to nod, shake their heads, or point.
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> 
> 

... and D&D Beyond - [Skeleton entry](https://www.dndbeyond.com/monsters/skeleton) states ...

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> Understands all languages it knew in life but can't speak
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> 
> 

... but both of these interpretations seem to be relatively 'new' 5e expansions to d&d skeleton lore. Wrt Habitual Behaviors in the 5e MM, if "skeletons of nobles might continue in an eternally unfinished dance" && "can load and fire a catapult or trebuchet".
Also, wrt D&D Beyond, it appears to be poorly worded. If taken literally, that it simply cannot speak; then it would be able to use sign language, portions of thieves cant, or write & still communicate.

I think all of the older versions are more consistent wrt skeletons in this respect; in that the creator can command them via magic (and it ignores the medium of the command.)

Therefore we need to break up your question:

1. Can it not speak because of its undeath?

If you look at all the lore in total, the answer here would be the skeleton cannot "communicate", speaking or otherwise. If you look at 5e literally, then the two sources are possibly contradictory & you'll have to subjectively decide for your world/campaign.

2. Could it learn to speak a language?

The simple answer is no... however, again looking at all the lore, should a different necromancer, demon, etc gain control of the skeleton; the method of control would give the ability to command irrespective of language.

Relatedly, an item of consideration is whether or not skeletons are deaf, & how their "vison" works.?. In my campaigns, skeletons are "unintelligent", and are deaf; with their "vision" being more animalistic/primitive in nature (they can't read, or understand complex items <missle weapons & doors included>)...

This isn't to say a specific necromancer couldn't craft a "unique breed" of skeletons that have different features, including higher intelligence; but just that the "average" skeleton does not.