Someone that sells, lets say beer, don't need to know how to brew beer to sell it do they?
That's a moot point. You sell beer in filled bottles, already tested for food safety at the manufacturer, so not much "health" concerns here. Of course, being learned about what you sell is going to make you look more professional. You could then advise a costumer about different types of beer, for example. As we say in my country, "knowledge does not take up space".
But what if you are preparing a personalized liquid for a costumer, or advising him about nic concentrations, and dealing with strong nicotine bases?
The example the OP gave is not even really a math problem. It's a complete lack of knowledge of how mixing different concentrations work. And that cannot end well if you're making something yourself, rather than just selling it.
Imagine a car seller who *obviously* knows nothing about cars. He "just sells" them, so he has "no need" to know more about them than the price tag.
Would that look professional to you?
ETA:
Suppose that I make a big, nasty cut on my forehead, and I go to a clinic to have it stiched.
Everyone in that place may well be the most professional people I could possibly find. But wouldn't I start questioning that, if the nurse who is welcoming me makes such a *stupid* remark as "You are losing too much blood. Next time, take your belt and make a tourniquet around your neck to stop the bleeding" ?
