Well, when you say something is a social construct it opens the door to find explanations for why that social construct has arisen. You open the door to questioning why those specific categories have been chosen. Why is it that in the early 20th century Italian was a race and now those people would be considered white (in America). It turns the conversation away from what is distinctive about a group and towards why we regard those distinctions as important.

> What are they trying to communicate about race?

That the hard racial boundaries are unscientific (despite attempts to make it so), and that it's artificial and depends on consensus, and therefore is subject to change, and is typically subjective to the involved social group: the "one drop rule" is an example of how arbitrary this can get.

As sibling pointed out, in the United States, Italians and Jewish folk used to be not white, but are now widely considered to be white, despite not having any genetic or cultural changes in the interval between the shift in categorization.

That racial categories and the criteria for deciding which category an individual belongs to depends on history, traditions and politics. There is no objective criteria to decide what constitutes a "race".