# Why does electromagnetic induction actually occur?

You are correct. Essentially it all boils down to the Lorentz force $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$. If you move into a frame of reference where the section of the loop is momentarily stationary, then you can do a Lorentz transformation to find out what $\vec{E}$ is in that frame. In that frame, $\vec{v}=0$ of course, so the second term is zero, but $\vec{E}$ will now be non-zero, and, in fact, equal to $\vec{v}\times\vec{B}$. In this frame, the force on the charges is purely electrical in nature, i.e., due to an electric field, and this is why you can define an EMF analogously to electric potential. But because wires are usually loops and each segment of the loop has it's own reference frame, there's no way to do this everywhere (globally).