Metaphor
Here is you problem
You assume the poor black kids are going to school with middle class or rich white kids
They aren't.
so, as a rule, you have children with the relative same socio-economic background going to school together. And now, with the current resegregation of a growing number of schools you don't even have black students and white students in the same school. Add to that that these schools are more likely to have inexperienced teachers and in some schools, teacher still working toward their permanent license, you get teachers easily rattled, even by three year olds and that isn't because of misbehavior of ghetto children.
What kinds of behaviours qualify a preschool child to be suspended is a different debate. But, lest my posts have been misunderstood, I want to make the following clear
i) Black preschool children are being suspended at a rate about 3x that of White children (this is not in disagreement)
ii) I think that 'suspension worthy' judgments will differ from teacher to teacher and school to school, and it probably has an unconscious race element
iii) Looking at the suspension rate difference between Black kids and White kids does not tell you whether there is a race element in teachers' judgments, because we don't know about the objective rate of suspension worthy misbehaviour difference
iv) Black children are born to younger mothers, into more single-parent families, into lower socioeconomic circumstances than White children, as well as a host of other Black White differences and all of which you would expect to increase the misbehaviour rate of Black children over White children
v) There could be a large Black-White suspension rate difference even if no single school actually had any race-bias nor did Black children misbehave more. That seems paradoxical but if schools are very segregated, and Black kids go to schools with higher suspension rates/more hair-trigger policies, then no single school would need to have a race-based element but Black suspensions would still be higher
vi) The data are consistent with a number of scenarios and I see no easy way to differentiate between their likelihoods without additional data.