I assume people are so appalled by the concept of physical punishment (which, let's be clear, I don't do and barely experienced either), that they don't want to acknowledge... how English works.
"Spanking" implies an open palm or maybe a belt or thin switch, on the rump. It hurts; it may leave a bruise; it may be barbaric -- but it doesn't involve serious injury (say, to internal organs). The point is to inflict pain without serious injury.
"Beating" carries no such connotations of limited harm. It can be done with fists or blunt objects; it can target the face or internal organs like the kidneys; it can be severe enough to lead to death.
This difference in meaning is as much about connotation as denotation, but the connotational differences are very large. You might say that, logically, a spanking is a kind of limited beating, but not all beatings are spankings.
So, as a matter of language, you're right.
This is in bad faith, a drug lord won't give you a spanking unless it's sexual in nature. I assume you know the difference between a sexual spanking and a beating in the street. Perhaps not. A parent can give a beating, but that is different from a spanking.
I think trying to equivocate a spanking with a beating is intellectually dishonest. If you can't tell the difference in both intent and intensity, I have no idea where you are coming from. You might be against spankings but to argue the words spanking and beating are synonyms is simply wrong, and quite honestly, juvenile in the level of reasoning. As the OP said, words matter.