I have a two wire system and after installing GFCI outlet in kitchen I realized there is a problem with some type of inconsistancy causing the GFCI to trip as soon as power is sent to it. Thinking the problem was in an older GFCI outlet I attemped to reuse I purchased and installed a GFCI breaker. Same problem. I'm thinking there is possibly a shared ground in the wiring as the kitchen, dining room and basement lights are all on this breaker. In previous testing while installing a new light I noticed some low voltage current coming through even when the switch was off. Is it possible to get a GFCI to work under these circumstances? There is one outlet downstream from the GFIC outlet. I installed a new conventional outlet in place of the GFCI after installing the GFCI breaker. Everything appeared to work fine with a 20 amp breaker and no GFCI outlet installed.
Sounds like the circuit is sharing a neutral with another circuit.
With your GFCI breaker installed, turn off all other breakers. Reset the GFCI breaker, which should now hold. If it does not hold, then you have a problem with the wiring on that circuit and need to open each box to investigate.
If the GFCI breaker does hold, turn each breaker on one at a time until you find the circuit that trips the GFCI. This is the circuit with a shared neutral.
You then need to open switch boxes, light boxes, on both circuits to figure where the neutrals were wrongly tied together. Suspect anything that looks like a homeowner addition, or fix. A common place this might happen would be in a switch box that controls different lights, with two or more circuits feeding the box. An unknowing DIY-er may have tied all the neutrals together.
I had this issue as well. It turned out that someone tied the neutral from a separate circuit into the the GFCI protected lighting circuit. They needed a 3 wire to make the light switch work properly. Not having a three wire, they used the neutral wire as the hot from the switch. Not having a neutral anymore they ran a short wire from the closest light to provide a neutral return, being fed from a different breaker. It took 3 hours of troubleshooting to figure this one out.