All words are completely arbitrary and spoken languages are never very logical anyway.
Here is an example of an ordinary sentence that is logically inconsistent with its desired meaning, "You use your credit-card only if you do not either have enough cash, or enough money on your debit to make a purchase."
Typically either-or sentences logically mean exclusive-or, which means that it is a true statement only if one, but not the other is true. An example is that if I said, "I will either do my physics homework, or my mechanical engineering homework today," then that would be a true statement only if I did one homework and not the other. In this sentence, "You are allowed either to have a dog or a cat in the apartment," then clearly what is meant is that you are not allowed both, but it it is not meant that you are not allowed to have no pets, which is what is technically being said if either-or has a consistent meaning.
In the first example I gave, what is being said would technically appear to be a not exclusive or gate, which means that it is true only if neither, or both conditions are true. So if words are to have consistent meanings, then that would mean that you use your credit card when you don't have enough cash or credit, OR when you DO have both enough cash and credit. Obviously that is not what was meant.
When I was younger I noticed inconsistencies like these in almost every sentence, and it f****d up my SAT scores because I couldn't tell what was being asked. Now I do not notice them as frequently. I guess it just took a couple decades for me to get used to what people mean when they say things.