Mr. Smith was a teacher and had his son as one of his pupils. After Erwin asked his father a question during class, Mr. Smith eventually told his son of a dangerous theory. Official history books being full of contradictions and mysteries, Mr. Smith believed that humanity's memory has been wiped out at some point, which might explain why there is no story or memories of the Walls' construction. This theory cost Mr. Smith his life, but encouraged Erwin to seek out the truth about the world's origins and prove his father's guess was correct.
Erwin has a discussion with Commander Pyxis where he mentions the conversation he had with his father as a child. A long time ago, Mr. Smith explained his theories about the government purposely censoring history and how it should have been impossible for the people not to orally pass down the real history of the world. Erwin would tell others what he had heard and this would which eventually lead to Mr. Smith's "accidental" death by the Military Police Regiment.
While on the verge of death, Erwin would suddenly lash out while hysterically repeating the last question he asked his father. This action would cause Levi to remember the commander's last words before leading the suicide attack against the Beast Titan. Levi would then choose to save Armin Arlelt with the Titan injection believing it would finally allow Erwin to rest.