The "I am not a synth" speech is given by Mayor McDonough shortly after the Sole Survivor enters Diamond City for the first time. The speech is presented on the stage near the back of Diamond City. The transcript of a portion of the speech can be found on McDonough's terminal, where he had composed it prior to its presentation.
Everybody? Everybody! I need everyone's attention!
I would like to address the subject that is on everyone's mind, and that is the disgusting article Piper has written...
Diamond City has stood united for over 150 years. And what keeps us united are two things. First, is the great green guardian behind me. The Wall. Our protector and our savior from the filth of the outside. And second, is our faith and trust in each other. The faith and trust that has given us prosperity, security, and education for every citizen.
I. Am not. A Synth. I am the same flesh and blood boy who grew on these streets. Who was born in a shack just down the waterfront to Martha and Patrick McDonough. And I will not abandon my city due to the heinous allegations of the press.
God bless this city. God bless the Wall!”