A commenter accuses me of "basing the whole of my political philosophy on the seating plan of the French Revolutionary Parliament" because I described someone as "not a lefty".
Twenty years ago, I was happily drawing Nolan charts, representing social liberalism and economic liberalism as orthogonal, and all sorts of other issues as being capable of being decided independently.
Back then, I saw politics as an intellectual pursuit, and policy positions as the result of analysing the justifications and effects of policies.
Meanwhile, on Planet Earth, actual politics was going on. Politics is about who has power, and you don't get power by being on the fringe. You do it as part of a dominant coalition. If you are serious about politics, you support all the positions your coalition holds, whether you really believe the arguments or not. Anyone who is not with the party is against it.
Therefore whether any given idea is placed on the left wing or the right wing may well be arbitrary from an intellectual point of view, but it is an ineluctable necessity from the point of view of a politician. If you are a left-winger in Britain or America today, you'd better support renewable energy and oppose nuclear. Maybe in a couple of decades today's left-wing policy will be a right-wing position, but that doesn't matter today. Also, you must only take as strong a position as the main left coalition does, because if you take a stronger position than them, you're an extremist, which is always bad. Again, an extreme position today may be moderate in ten years, or vice versa, but there is a moderate-left and a moderate-right position on any issue, defined by the two coalitions competing for power.
If you really have strong policy views of your own on a particular issue, you can try to change your coalition's position on that issue, but if you don't hold with your coalition, you're not doing real politics.
For that reason, there always are just two sides that matter, and those two sides each have a position on everything. So it makes perfect sense to describe politics in terms of "left" and "right", in the eighteenth century, the twenty-first century, or arguably even, as Alison Plowden does, in the sixteenth. Any given policy position might be left-wing in one country or one generation and right-wing in another, and the main axis of left-right opposition might be social policy, economic policy, or foreign policy, but there have to be two sides.
Related: Fascism: Right or Left