We will never hear the end of this whilst the DVLA persist in referring to VED as "tax" and "tax discs" all over their reminders and website.
That is after all where motorists see it most.
Provided they continue to call it "car tax" and not "road tax" I can't really see the problem there. It's a tax on cars, you only pay it if you're in a car, sorted.
Driver: "You don't pay road tax"
Cyclist: "Nor do you, you pay car tax. Does this look like a car?"
D: "I pay to use the roads, you don't "
... at this point you can choose
C1: "I pay council tax, income tax, VAT and a pile of other taxes, all of which are spent on roads"
C2: "Nor would you if you didn't have to, so that actually makes you dumber than me not better than me"
C3: "I bet you pay for sex too, I don't"
or other rejoinder of your choice. If they get onto "roads are for cars", the reply "no, streets are for people" is often apposite, at least in builtup areas.