Why does Bud think the man in the flyer is his father?

Bud believes the man in the flyer is his father because he sees a resemblance between himself and the man’s picture, particularly in their facial features. Additionally, the flyer suggests that the man is looking for his son, which gives Bud hope that he might finally find the family connection he's been longing for. This desire for belonging and understanding his roots drives Bud to pursue the man depicted in the flyer.