This quotation from Part I, page 33 occurs when Coates discusses his experiences as a child in the school system. Coates sees the streets and the schools as two arms of the same beast. If a kid slips up on the streets, he will get hurt. If he fails in the schools, he will get suspended and then sent back to the streets, where he will get hurt. Then, society can give up on him without guilt and say he should have stayed in school. Collective society will remove itself from any responsibility for the child’s well-being. So, when Coates says ‘good intention’ here, he is speaking of all the people involved in the trap between the schools and the streets. His individual teachers may have had good intentions, but that doesn’t help him in any macro way. The problem with good intentions is that they don’t accept true responsibility. It is a passive way of justifying the large numbers of black children who fail out of school and end up on the streets.
The second part of this quotation references “the Dream.” Coates has already described the Dream as being an idealistic view of America, in which the country is helpful and innocent. He points out that nobody is going to openly say they want to keep black people on the streets. But also, nobody wants to take personal responsibility for figuring out the problem of the black ghettos. Teachers preach about personal responsibility and how it will make you into a good person and keep you out of jail, but that talk doesn’t line up with America’s “criminal irresponsibility,” that has condoned generations of violence against black people.