Irrotational flow must have a velocity potential due to the Helmholtz theorem, which states that if a vector field is irrotational, it can be expressed as the gradient of a scalar potential. The discussion emphasizes that if the curl of a flow is non-zero, it indicates that a potential function does not exist, as the curl of a gradient is always zero. The relationship between irrotational flow and velocity potential is crucial for understanding fluid dynamics. Additional resources were shared to further clarify these concepts. The conversation highlights the foundational principles of fluid mechanics related to irrotational flow and potential functions.