I fully agree that weighing is better, but if you apply your standards to weighing you'll end up concluding there's also no such thing as "weight measurement."

- The so-called "weight" will differ depending on the type of scale and how it's used. People used mechanical kitchen scales just fine even when some measured a bit less and a bit more

- While digital scales can be more accurate, accuracy can still vary, and of course the reported weight can vary depending on where an object is on the scale or how the scale is set up. (Yes, I've used a scale that wasn't on a smooth flat surface. It worked out fine.)

- "Dry materials" like flour are hygroscopic, and even though weighing is better than measuring by volume, you end up weighing the flour + water, when what you want is just the weight of the flour (e.g. you may have to consider the storage history of your flour)

- There's the ~0.4 % weight difference between the equator and the poles.

Yes, these are all very picky, but that's how your "no such thing as" comes across to someone who grew up using volume measurement in the home kitchen.

Instead, simply say that weight measurement results in more reliable and predictable cooking. Perhaps also add that cleanup can be a lot easier when ingredients don't need intermediate staging.