I believe the "explanation" used to justify saying "CCP" in the West is that the Chinese diminutive for "中国共产党" (Zhongguo Gongchandang, Communist Party of China (but which can also be understood as Chinese Communist Party)) is "中共" (Zhong Gong, so "Chi(na/nese) Com(munist party)"). Thus, Western media argues that, to preserve the order in which the words appear, "CCP" is a more appropriate term. Of course, it doesn't make sense to preserve Chinese word order in English because, newsflash, Chinese is a different language than English; and the CPC's official name in English is "Communist Party of China." So this is just a thinly veiled excuse to disrespect the CPC by calling them by a different name.

As for the reason why the English translation of "中国共产党" is "Communist Party of China" and not "Chinese Communist Party," this is because the Comintern required parties to follow the name of "Communist Party of (Country)." There are many exceptions to this rule (the Socialist Unity Party in the GDR comes to mind), and of course the Comintern no longer exists, but the CPC respects it to this day.