Why do electromagnetic waves detach from the antenna?

The build up of Maxwell's equations was long, and the experimental confirmation that light is the electromagnetic waves predicted by them took a while. There are "laws", relations which were defined from experimental observations, which are as an axiomatic underlayer so that the equations appear consistent and give the electromagnetic wave as part of its solutions, which eventually fitted light observations at the time. It also explains mathematically the classical electromagnetic wave from an antenna.

In classical electrodynamics , a changing current generates electromagnetic waves. A moving charge with a constant velocity is a current of charge.An accelerated charged particle is a changing current and thus has to give off electromagnetic waves according to the equations. That is how antennas work, by changing currents. At the time the current carriers were a hypothesis.

We now know that they are electrons and positive ions, depending on the set up. At the quantum mechanical level, a change in velocity for an electron means an interaction with the field , either giving up energy or radiating energy away and there are QM precise calculations on the probability of an accelerated electron to radiate a photon. There is continuity in the theories of physics and it can be shown mathematically that a confluence of photons builds up the classical electromagnetic wave of Maxwell equations.