First there's the issue of a neonate needing no training. There are literally hundreds of studies that show that the sort of baby talk that infants are exposed to has a clear tendency to be just a little ahead of the child's own development. This 'motherese' tends to have exaggerated intonation, simplified grammatical structure and vocabulary, combined with repetition, questions and rehearsal of key aspects of language. This just happens quite naturally, without planning and so it's easy not to notice just how much effort, practice and exposure a child is involved in. The fact is that as some poor sods discover, simply planting a child in front of a TV or radio does not allow them to develop language. It's interaction with carers.
I have only three words.
Poverty of stimulus.
The acquisition of syntax is accomplished with an incredibly sparse amount and many times poor quality of data.
It is not acquired through learning. There is no possible way it could be.
That is beyond dispute.
Again, you completely misunderstand what Chomsky has been saying. If you listened to him in the video, you would have caught where he said that learning from stimulus was absolutely necessary. The thing you are missing here is that nobody who studies this topic seriously disputes the fact that language is instinctual in humans. What is in dispute is what is learned from experience and what is biologically inherited. Chomsky also jumps to a conclusion that some of us have serious doubts about--that the purpose of the linguistic "grammar" is to generate well-formedness intuitions. A more behavioral functionalist approach to language (and one that I favor) is that intuitions are a product of a general introspective capacity that predictively models sensorimotor behavior. So the evolutionary "purpose" of the psychological grammar is not to enable intuitions of grammaticality, but to produce and understand linguistic expressions. Such intuitions are simulations produced by a more general cognitive function. (One of the questioners in the video seemed to be thinking along these lines, but he didn't pose his question in quite the way I would have.)
I suspect that most of what I say bounces off your defensive shields, unter, but maybe others who bother to follow the discussion are interested. I'll just make one more remark about a flaw in Chomsky's approach to universals. He referred typological universals, but he used the somewhat dated expression "Greenberg's universals", referring to the linguist who laid some of the seminal groundwork. An example of such a universal (which Chomsky should have mentioned to help his audience understand what he was talking about) is the tendency of verb-first languages to have prefixes and prepositions, and verb-last languages to have postpositions and suffixes. Another would be that it is very common for verb-first languages to place modifiers after the words they modify and for verb-last languages to place modifiers before the words they modify. (I have greatly oversimplified this, but you get the idea I hope.) Chomsky also thinks in terms of other types of universals--e.g. his principles of binding theory. The problem is that he has no principled method for separating biological universals from accidental ones. So, if a nuclear war wiped out every linguistic community except for a community of Amharic speakers, then every feature of Amharic would become a linguistic universal overnight. However, not every feature would be biologically determined. And that is a big problem for him, because the dispute has never been whether language was to some degree innate, but what aspects of it were innate or not innate. It is not enough to merely say that certain universals are evidence of UG. One needs to be able to say
which universals (if any) are evidence of UG. Otherwise, his claim becomes a "just so" story.