The counter-example (Person C who understands person B's difficulties) is displaying empathy
empathy (n) The ability to identify with or understand another's situation or feelings.
If I were writing your sentence, I'd simply say that your person A displays "a lack of empathy" toward's B. It's clear and understandable.
Personally, I've never understood the fascination with squeezing things down to one, rare and hard-to-understand word when two simple ones would get the message across much better, but if you absolutely cannot use the spacebar, you can use the form "unempathic", simply by adding the "removal" prefix un- (as in "uninterested", "unfeeling", "unmoved").
Personally I prefer the "lacking empathy" form, as there are other "un-" words formed from positive roots that carry a hint of being opposite, rather than just lacking (see "unholy", "unfriendly", "uncharitable").
A warning: although the "un-" prefix will make the meaning reasonably clear to the reader, no reputable online dictionary lists this word.
"unempathic" does show up in writing, although far less often than "empathic" (Google ngrams says there's a 100x difference, although it does have instances of "unempathic" dating back to the 1950s)
is there a different word meaning "without empathy"?
Despite it's Greeky-ness, "empathy" is actually quite a new word, and it's not Greek, but German. "Empathy" entered the English language as fancy translation of a German word einfühlen, which was coined by philosopher Rudolf Lotze in the 1850s from a literal translation of the Greek "en" and "pathos" (in, feelings) -- this is why the word "reverted" to "Greek" when translated into English.
einfühlen: to put oneself in someone's position, condition, etc.; to understand something inwardly, to empathize with it
(Lotze must have had a specific meaning in mind to create a new word, because German already had a word for this: nachempfinden )
Unfortunately, none of these three words have a single-word antonym with the sense of being unable to see the world from someone else's perspective.
Ironically, Greek does have a similar-sounding word to "en-pathos", but it means "hatred", which just goes to show that sometimes a word you keep using really doesn't mean what you think it means.