The speaker of "Incident" is an African-American man (at least, we're assuming that it's a man, based on Countee Cullen's use of the first person "I"). He is looking back on a moment in his youth. In a way, it's almost like we have two speakers in the poem. We have the current-day speaker, who recollects a moment from his childhood, and the speaker as an eight-year-old boy, who is living that moment.
We're not suggesting that our speaker has multiple personalities or anything like that, but we do think it's important that the speaker (as an adult) manages to convey the power of the racist incident that so defined his (young) life.
And let's not forget the way the speaker speaks: he's a straightforward dude who doesn't mince words. The poem is straightforward and direct; you won't find any fancy metaphors or over-the-top poetic diction here. Our speaker aims to speak clearly and directly in order to impress upon his readers the shock and outrage that he once felt. And that's exactly what he does.