Recall that because it's getting energy from the nucleus rather than from electron shells, there is 2,000,000x more energy in the mined raw material when you're using nuclear. That's why a train car of nuclear fuel per year can power a city, where a coal plant needs a mile-long train car per day. Nuclear energy density is crazy high. So you don't have to mine a lot, you don't have a lot of waste, you don't need lots of land, and you don't emit any carbon dioxide.
I say carbon-free for anything that's under 40 gCO2-eq/kWh (so I can include solar), which is 10x less than natural gas, 20x less than coal. Nuclear is 40x less natural gas! It's the lowest carbon energy source we know, tied with wind.
We do need to provide meaningful feedback to things that are incorrect, such as the suggestion that nuclear is not tied with wind as the lowest-carbon full-lifecycle energy source we know.
I chose to work in the nuclear industry specifically to help avert climate change. I was like: "I want to help reduce climate change. Aha, nuclear is interesting because it's low-carbon and also not perfected. That's a good challenging problem to work on!"
This doesn't invalidate anything I've said. In fact, it bolsters things I say because it means I know what I'm talking about.
That's fine and you're free to do that, but it doesn't make what I said "incorrect." The uranium cycle uses carbon and, what's worse, produces vast amount of tailings (radioactive waste) which contaminate land and water. This is in addition to the spent fuel rods which most people think of as "nuclear waste." I hope that you could agree that those are true statements.
Nuclear fission is neutron + uranium = fission products and energy. This process is literally carbon-free. Solar PV is photons + semiconductors = electric current. This is directly carbon-free. Wind is wind + blades = mechanical motion. This is directly carbon-free. Coal, natural gas, oil, and biomass are Carbon + heat in the presence of oxygen is CO2 + energy. These are not carbon-free. This is the purpose of the term carbon-free.
Now, literally everything has non-zero carbon lifecycle costs as long as we are using carbon-derived energy in our infrastructure. It is impossible to be fully carbon-free with coal, natural gas, oil even if all your infrastructure is electric. With solar, nuclear, wind, etc., you can get to a truly carbon-free lifecycle if you work hard to electrify or otherwise clean up your trucks.
Meanwhile, today, nuclear lifecycle is the most carbon-free overall, tied with wind.
The term carbon-free is used colloquially to mean anything that doesn't directly make carbon alongside energy. It is right and proper to point out lifecycle carbon costs too, and again nuclear is tied for lowest lifecycle.
Nuclear is the most carbon-free thing we have. You bet it is advertising. It's truthful advertising of the positive characteristics of nuclear energy. People have a right to know how carbon free various energy sources are.
But people DO claim that wind, solar and hydro are 'green' or 'carbon-neutral' or 'carbon-free' energy sources, so it's fair to hold nuclear to the same standards. And nuclear more than meets those standards.
Only enforcing those standards for nuclear feels like an isolated demand for rigor.
Breathing produces carbon dioxide; so you aren't going to get very far with that sort of argument. Nothing is carbon free.
The heavy equipment is not going to produce enough carbon to be worth measuring on a per kW basis. The energy density of nuclear fuel is just too high.
See: https://www.xkcd.com/1162/