Folded dipole - how does it work?

The distance (measured along the wire) from a feedpoint to the geometrically closest point on the other parallel part is lambda/2, so there is a phase shift of Pi radians between waves radiated by the two parallel parts. So they should cancel each other due to destructive interference.

keep in mind that the currents at the ends is zero on both sets of parallel wires. The two sets of wires form a sort of impedance transformer. I cannot remember the math, but they counteract each other in the impedance area and this is why the bandwidth of the input impedance is wider than with ordinary one wire dipoles.

For more information about the radiation of Folded antenna you can use Antenna book written by Balanis (capture 1, page 18, Edition 3). any flared transmission line could radiate.