Actually I don't have a clear-cut favourite. Candidates:

the very versatile way in which natural language allows sentences to be abbreviated
for example, conjunctions distribute across word categories: John likes Mary and Pete likes Mary abbreviates to John and Pete like Mary. Cool. Standard mathematical logic doesn't allow this, although it has similar features. Perl, with its lists, comes close.
actions and states of affairs are syntactically identical in natural language
and conjunctions can express a huge variety of logical, temporal, causal and other kinds of relationships between them: John likes Mary and decides to help her, Hurry up or you'll miss the bus, I ran and caught the bus, You're dead meat and you know it. By contrast, many imperative programming languages rigidly separate actions and logical conditions, and have very rigid rules on their combination. Features like conditional AND and logical connectives applied to statements alleviate this; Perl includes more, similar features, and succeeds in being much more natural in this regard, without losing its sense of grammar. Declarative/Logical programming languages on the other hand pretend that everything is a conjunction of logical statements and all execution order is a matter of implementation. It isn't to us humans.
subclauses around gerunds
deliberante senatu, periit Saguntum, mutatis mutandis, stante pede. English has similar constructs: considering their power, these constructs are an asset to the language; Dutch has a more limited range, so we must use clumsy relative clauses to express things like All things considered or Grammar being what it is or Having seen the problems this can lead to. Take it from a Dutchman: English is cool, but Latin sizzles!
recursion, repeated application of a process of sentence or word formation
This is more common in German and Dutch. Examples: Ik zou jou hem dat wel eens hebben willen zien helpen repareren ('I would have liked to see you help him repair that') or heteluchtcirculatieverwarmingsonderhoudsmonteur ('hot air circulation heating maintenance technician')

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