I think sometimes confusion arises when people discuss 'race' because they mean different things by the same terms. For example, when some people say, "Caucasian", they mean people with deep-set eyes, high nose bridges and more body hair. Their definition of 'Caucasian' includes not just white Europeans, but also people from North Africa, West Asia, Central Asia and South Asia, some of whom are very dark-skinned. Yet many other people use the term 'Caucasian' to refer to white Europeans only. They don't consider Indians, Pakistanis and Sri Lankans as 'Caucasian', even if these South Asians have Caucasian facial features. To them, 'Caucasian' is limited to light-skinned European-looking individuals.
In the US, some West Asians and North Africans (or 'Middle Easterners' in popular terms) occupy an ambiguous space. Census categories count them as 'white Caucasian', but the majority of European Americans (even those without prejudice against Middle Easterners) don't see most of them as 'white'. So, they are 'Caucasian' but not 'white', at least to some people.
I'm not saying which terms are 'right' or 'wrong'. I do have my opinions on what makes sense and what doesn't but others are entitled to theirs. I personally find it a little odd when folks mention 'Black', 'Caucasian' and 'Asian' in the same breath, as if they are counterparts to each other.
If we're going to be discussing color, then the counterparts of Black should be Brown, Red, Yellow and White. Caucasian is not quite equivalent to 'white', for reasons mentioned above. Nor is Asian equivalent to 'yellow' - as Asian populations include people who are white-skinned, like many Iranians, Turks and Armenians as well as people who are black-skinned, like many South Asians and some Southeast Asians. 'Asian' is not a 'color term' or a 'racial term' - it denotes geographical origin, at least by Webster's Dictionary's definiton.
'Caucasian' and 'Asian' are not counterparts to each other either. 'Caucasian' makes sense when discussing 'race' within the old tripartite racial classification system of Caucasoid, Mongoloid and Negroid (now discredited because large segments of the world population don't fall into the stereotypical sets of attributes assigned to each category, though people still find it useful for the purposes of discussion.). 'Asian', as mentioned previously, denotes geographical origin, not physical attributes, though many Americans use it to exclusively refer to yellow-skinned, 'Mongoloid-type' East Asians/some Southeast Asians.
The reaction of South Asians in America to this has been varied. Some consider themselves 'Asian' regardless, others accept the majority definition and say, "I'm not Asian, I'm Indian." But many members of indigenous populations also self-reference as 'Indian' - some find the term 'Native American' offensive since their nations existed before there was an entity called 'America'. So there exists potential for confusion. American Indian and Indian American mean two different things.
Frankly, as an individual of East Asian origin (and I don't claim to speak for all East Asians), I'd rather have people use the term 'yellow' when discussing Mongoloid-type East Asians, instead of using the terms 'Asian' (unless the speaker is using it to refer to all populations of Asia, and not just East Asians) or 'Oriental'. The way the term 'Asian' is used in the United States inaccurately excludes a significant part of the Asian population. And the term 'Oriental' does have Eurocentric implications. The United States is east of Japan, so it would make sense for the Japanese to call Americans 'Orientals', if one were to go that route.
Of course, some people believe that 'race' should not be discussed at all, thus eliminating the need for 'racial terminology'. But I think it is inevitable that people in different regions would develop general trends in appearance (although exceptions will always abound since human populations move around) and people would come up with terms to describe these differences.