Confusion in understanding characteristic impedance and input impedance of an open circuited transmission line
If the transmission line is either infinitely long or terminated with the characteristic impedance, there are no reflections back to input port so input impedance equals characteristic impedance.

If you have reflections, like in the case of leaving transmission line end open, signal reflects back from the end to input. So the signal being fed to input port not only drives the transmission line but it has to drive against the reflected wave too. Phase of reflected wave depends on time travelled on the line and thus the length of the line, so this is why the input port appears to have different impedance based on transmission line length.