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as you know in a transmission line the current flows equal and opp because of the interaction between the two lines... when you open circuit such a line then current has to flow through it any how since the current flow is only due to the interaction between the lines.... and when you make a dipole antenna out of it even though there is no interaction between the lines and the ends where they are bent in opposite directions...then current still flows because there has to a same current as there is interaction throughout the rest of the line...hence a current has to flow if it has to satisfy kirchoff's law...
An open circuit is an infinite resistance. That is the same that an infinite impedance at 0Hz.
In an antenna, you hate to think in frequency. At high frequency, an open circuit is not an infinite impedance.
For example, a capacitor is an open circuit, that represents an infinite impedance at 0Hz, but at high frequency it behaves as a non infinite impedance. It's the same for antennas.
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