why are copper lines faster than fiber lines in terms of latency ?

The index of refraction of a typical optical fiber is about 1.48. Light in that medium travels at about 2/3 c. Also light doesn't necessarily take a linear path through the fiber. Add to that the latency in the transducer circuits at each end. The velocity factor for data cables ranges from 0.4 to 0.7, 0.8 for coaxial and twin-lead transmission lines, and 0.95 for ladder lines. For standard category 5 data cable, it's 0.64. Any difference between that and fiber is mostly interface circuitry, router delay, and so on. None of the speeds are greater than the speed of light in vacuum.

the speed of signals in most cables that i have measured is about 8 in/ns. look up the index of refraction of a fiber optic and see how fast it is. If the fiber is faster but you have to convert its optical signal to an electrical signal and that process is slow, even if the optical fiber is faster the system will seem slower than a copper based one that could use the signal directly.

That is for signal transport alone, if you are sending a lot a data however, the optical signal has to win because it can support 10^15 Hz carrier frequecies, and therefore way more bandwidth.

What's your source? Is it that the equipment is slower? Seems a little unlikely, unless it is a consequence of the upper layers, eg MAC & networking protocol delays.

With copper, eg pairs, the information is transferred in the group velocity. This won't be faster than light & can be slower by a good margin.