One port Vector Network Analyzer (VNA) Calibration without the given standard Calibration Kit
Why is the arc caused in the first place? Is it because of fringing capacitance (inductance) for open (short)?


It's because the cal standards you used don't match the expected behavior of a nearly ideal open, short, and load exactly.

Most likely either the open or the short has a small amount of distance between the SMA reference plane and the effective position of the reflection. 

It may even be that the standard short (for example) has a small, but known and accounted for, delay between the reference plane and the actual reflection plane, but the short you cal'ed with doesn't, leading to a negative delay in your "calibrated" measurements.

Another issue could be that you said you're using an SMA cable, but told the VNA you were using BNC cal standards. The BNC cal standards might be significantly different from the SMA devices you used (for example the definition of where the reference plane is in a BNC connector is likely noticeably different from where the reference plane is in an SMA connector), and this is causing the calibration to be inaccurate.

Another issue could be that BNC connectors are usually only characterized for up to 1 GHz, while you were calibrating for 4-6 GHz. If the models for the BNC standards are only accurate up to 1 GHz and the machine extrapolated the performance out to 6 GHz, it could have wildly inaccurate model for how the standards (either BNC standards or the SMA devices you used) behave in the range you measured. 

So I'd suggest:


If possible, use the proper SMA cal kit to calibrate an SMA connection.
If not possible, at least use the SMA cal kit model when cal'ing with SMA devices. But expect a few percent (of the Smith chart unit circle) error in the final measurements.