What is the reason for starting before the traffic light turns green?
The "early start" allows cyclists to clear the junction ahead of motorists, this is useful for cyclists making off-side turns (right in the UK, left in the US). It also helps cyclists going straight on avoid conflict with motorists making near-side turns (left in the UK, right in the US).

The UK and many places in Europe have Advanced Stop Lines (Highway Code rule 178) at traffic lights:



These allow cyclists to get ahead of motorists without jumping the red light.

For junctions without an Advanced Stop Line you'd have to weigh any benefits of clearing the junction against the potential legal consequences, the likelihood of increased driver hostility and the risk of colliding with a vehicle jumping the lights from another direction.

Personally, I don't jump red lights. On the roads I cycle on I think it would be more dangerous than waiting for them to change.