Pathos is defined as an appeal to the audience's emotions and is considered a persuasive technique. The author of a speech uses images or stories that his /her audience can sympathize with in order to win their approval for his/her main argument.
"A Talk to Teachers," published in 1963, was originally delivered as a speech, "The Negro Child - His Self Image", the same year. In the paragraphs that you mention as well as throughout the speech, Baldwin appeals to his audience using both techniques associated with pathos: using metaphor or storytelling and the overall emotional tone which conjures up images with which the audience can relate to. Paragraph 3 starts with a strong emotional sentence
any Negro who is born in this country and undergoes the American educational system runs the risk of becoming schizophrenic.
Baldwin explains his powerful statement by making more references to images that he is certain will have a strong hold on his audience as they convey America's national myth of freedom and social mobility. In his second appeal to pathos, he says that, on the one hand, the African American child is born "in the shadow of stars and stripes," a symbol that guarantees liberty for all and the possibility to improve one's social standing ("He is part of a country in which anyone can become president, and so forth"). Yet, on the other hand, he is also consistently reviled by mainstream America as part of a race with no cultural or social heritage:
his past is nothing more than a record of humiliations gladly endured. He is assumed by the republic that he, his father, his mother, and his ancestors were happy, shiftless, watermelon-eating darkies who loved Mr. Charlie and Miss Ann, that the value he has as a black man is proven by one thing only – his devotion to white people. If you think I am exaggerating, examine the myths which proliferate in this country about Negroes.
In this quote I have italicized what I consider another appeal to pathos: the institution that Americans often cite as a source of national pride, that republic which they built in opposition to the colonial monarchy, is the very source of stereotypes and discrimination against African Americans. Baldwin's implicit statement here may also refer to the trauma of the Civil War: what was the use of the Civil War if the state continue to perpetrate the stereotypes that were part of the slave-holding culture of the South?
In the last paragraph mentioned in your question, Baldwin makes his appeal to pathos by telling a story, reminiscent of his own childhood experiences, to prove how an African American child who ventures outside his neighborhood into the city understands his inferior and unequal condition.
It was very details