Consider a single finite length wire, bent in an L shape, 1/4 wavelength of some given frequency F0 from the end. A current impulse, say driven by a single spark from a spark transmitter, will indeed be seen traveling in the reverse direction at the corner of the L at time roughly half the period of F0 later. However this "bounced" current impulse will be reduced, due to a portion "lost" due to wire resistance plus EM energy loss due to coupling into free space (or any nearby or distant conductors). This loss is usually less than 100% for typical wires of typical lengths in free space.
Now add another L shaped conductor nearby in a mirrored arrangement. SomeA portion of the "bounced" current might flow as displacement current across the two L corners to the other 1/4 wavelength L stub, due to the mutual inductive field.
So some of the current (the portion not "lost" and not sent a displacement current) indeed flows back down the feedline, which, summed with any current send up the feed line, adds up to a total current to voltage ratio, which we can call the resistive impedance of the feed point.
Now consider a sinusoidal drive of frequency F0 to be the sum of a bunch of these impulses (infinite in number, infinitesimal in size), modulated in amplitude by sin(F0).