No he didn't. Simplified, his statement reads "Ironically, those who defend government start by listing a thing provided by government that is a small facet of what they do".
There's no irony there, no juxtaposition, no opposite. He's trying to get across the gist of "why the hell is it always roads!?", but it's frustration, not irony.
It is ironic that the chief reason trumpeted by proponents of government action turns out to be a relatively part of their operations. It does the opposite of support their intention and presents a juxtaposition of what they think is a really good argument and what it actually amounts to.
It would be like if I claimed male authors were better than female authors, then cited George Eliot as my first example of a great male author. That would be ironic.
Your analogy doesn't work - because George Elliot is a woman. George Elliot isn't "a small part of the whole" of male authors, she's an exact counterexample.
Roads-by-government are "a small part of the whole" - they're not contradictory in any way to the idea that services are supplied by government. They're not a counterexample. It would only be ironic (and would also fit your example) if the roads in question were actually provided by private enterprise.
Well the roads are usually provided by private enterprise, though paid for by the state. But it is still ironic because the argument is not no government vs. big government, it's small government vs big government. Citing the roads is not a point in support of getting the government more involved in public life, because if maintaining the roads and other things like that were the only actions required by government, then the government would be miniscule.
What would not be ironic would be something like 'ironically, the defenders of government always mention the military as their first example - I mean come on people, have some imagination at least!' That would just be frustration.
Put simply, if there's a range of possible examples people can pick to support a given stance, and they always seem to pick one of the weakest/least-appropriate ones, then yeah, that's ironic. It's a state of affairs or an event that seems deliberately contrary to what one expects.
I think you're just trying to salvage an incorrect application of the term, and I don't think we're going to get much further here.
As an aside to that, your last phrase a state of affairs or an event that seems deliberately contrary to what one expects highlights a significant difference between British and American irony. In the US, you can choose to wear an ironic t-shirt. With British irony, you can't - irony is something that is unintentional (it can be known, just not intended). As soon as you intend to do it in any way, it's deliberate or expected and so becomes unironic.
I've heard British people claim that American's don't 'get' irony but i've never heard it claimed that there's a difference between 'American and British irony.'
In my experience the irony police are usually unwilling to consider the full subtext of someone's statement when they describe it as ironic. For instance people often say things like 'ironic, isn't it - beautiful weather all week and then when we finally decide to throw a barbecue, it rains. ' This is of course just bad luck, but people like to jokingly invoke some sense of fate conspiring against them. Or, someone might consciously wear an 'ironic t-shirt', and people consciously recognise the intent, but the unspoken subtext that maintains the irony is that there is some other observer or potential wearer who would be unaware of the incongruity.
the use of words expressing something other than their literal intention
Nope, doesn't qualify
A statement that, when taken in context, may actually mean something different from, or the opposite of what is written literally
Don't see how this works either.
I'll skip over Socratic irony and Dramatic irony- hopefully it is obvious this is neither.
I could be wrong, of course. The colloquial & popular use is so different from the actual meaning of the word, I am never quite sure I have the right of it.