The issue here is one of values and of putting those values into practice.
Curriculum inevitably grows out of a culture’s prevalent values. Contemporary education critics associated with multiculturalism look at the past value systems in America and elsewhere and see those systems of thought as tending to favor certain groups (often white males) over other groups (minority groups). So, “multiculturalist” education reforms seek to better align curriculum with contemporary values that recognize the importance of cultural diversity in adolescent development (and in wider national discourse).
The Edchange project offers this explanation in an article, "Stages of Multicultural Transformation":
The curriculum of the mainstream is Eurocentric and male-centric. It ignores fully the experiences, voices, contributions, and perspectives of non-dominant individuals and groups in all subject areas. At this stage, all educational materials, including textbooks, films, and other teaching and learning tools, present information in a Eurocentric, male-centric way. This stage is harmful both for students who identify with dominant culture and those from non-dominant groups.
The basic idea is simply that for a long time our schools perpetuated a point of view that envisioned a social hierarchy.
Here are a few examples of common criticisms. Telling the history of America from the European point of view, US school systems were choosing to mute alternative points of view such as those from Native Americans. By choosing literature for class use that focuses overwhelmingly on characters of one ethnic background, students from other backgrounds are unable to see themselves and their heritage validated in the cultural experience of reading. Critics also suggest that the situations--hypothetical and real--that tend to appear in textbooks and on standardized tests are skewed toward certain social norms and expectations, and as a result minority students are alienated by the system and at a disadvantage on high-stakes tests.
The critique that animates “multiculturalist” reforms is based on a social and political ethos that sees challenges to equal rights and equal opportunity as being built into any curriculum that implicitly favors one demographic group over another.
“Multiculturalist” goals for school reform align with a contemporary outlook that encourages diversity, promotes respect for and acknowledgement of difference, and (often) seeks to challenge any system that diminishes these things.