We talk about things being political, and political literally means what has to do with the polis, the city, the society of citizens (in one sense or another). It's clear that our usual use of the word does not really mean this; by it we mean not all that comes with citizenship but all that comes with elected or appointed offices of governance. But I think it's also clear that the older meaning is still there as a common secondary meaning.
In this sense, it's interesting to contrast the fate of the term 'political' with the term 'civic' (or 'civil', as we sometimes find it, although more commonly civil is to civic as polite is to political). In a sense you would expect them to be the same -- civitas is a rough, but natural, Latin equivalent for Greek polis -- but they really aren't, and that is because 'civic' seems to have headed (more slowly) in the opposite direction from 'political': the civic has more to do with the society of citizens, and usually not with the elected or appointed offices of governance unless we're talking about local govenments. (It still retains some connection with 'city'.) But the boundaries here are much looser, I think, than in the case of the primary meaning of 'political'; 'political' is often used as a sort of opposition to the society of citizens (abstracted from elected and appointed offices), while 'civic' rarely is. And, of course, in much of government, 'civil' positions are the opposite of 'political' positions: the latter are elected or appointed, while the former are hired.
The fact that 'political' has these ambiguities -- a specialized primary sense and a more general secondary sense that occasionally pops up, can make it difficult to determine what people mean at any given point when they talk about the political, and I think this often creates serious and troubling equivocations. 'Everything is political' if we take 'political' in the secondary sense, in the sense that is closer to what we usually mean by 'civic' -- directly or indirectly everything is civic, and it is as citizens (whether of cities, states, nations, or the world) that human beings achieve their highest natural goods. It is in this sense that man is a political animal, and it is in this sense that being a political animal both follows from and necessarily presupposes being a rational animal. Other animals are members of societies; only human beings actually become citizens of societies. It is a distinctively human spin on membership in a society. On the other hand, 'everything is political' is dangerous nonsense if we mean it in the primary specialized sense of 'political', which in the modern world has to do with political parties, into whose hands we ultimately end up committing elected and appointed political offices. We are not political animals in this sense; and in this sense it has very little to do with rationality. And clearly you are going to understand 'everything is political' in a very different way if you are thinking of the whole body of citizens working together as citizens than if you are thinking of politicians as legislators and magistrates.
What worries me somewhat is that I think there's an argument to be made that the ambiguity of the word 'political' -- which is a far more common word than 'civic' -- is a symptom of a collapse in our civic understanding. The ambiguity of the word encourages an equivocation that seems actually to be very common: that the only way to work together as citizens is by means of political offices or parties, which, again, get their power from the fact that we really think of political offices in partisan terms. This removes the emphasis on finding ways to work together (which does not always mean compromise in our usual sense, but sometimes means deference or even argument) and puts the emphasis on organizations which tend to be groups of citizens trying to shut other groups of citizens out of power. The one can't completely eliminate the other in a society that is still functioning -- when the partisan political completely abolishes the civic political we have civil war. But thinking of our political lives in terms of political parties more than in terms of citizenships is simply and utterly a deterioration, a degeneration, a fall. Political parties exist for the sake of political offices; political offices exist for the sake of the whole society of citizens precisely as citizens. When we take them as an important part of who we are, rather than affiliations for better expressing our positions as citizens, we have perverted what it is to be political.