Who has the right of way when I'm turning left on a solid green light, and the vehicle from the opposite side is also turning left?

I understand what the instructor meant by claiming the intersection. Entering the intersection to establish presence because when the light turns red other traffic is supposed to wait till vehicles in the intersection have cleared it.

Be advised, in some states this is not legal. A car entering the intersection is supposed to be able to clear it before the light changes.

The key to the solution is how opposing cars making left hand turns are supposed to travel. Please check the drivers hand book for your state on this. That said, this in one time when the traffic traveling against you is supposed to pass on the right and not the left. The turn is supposed to be made short of the center of the intersection. So both cars share the right of way.

That said- a left hand turn can only be made when safe to do so. They yield to all other traffic in the intersection. Getting hit while making a left hand turn is often seen as being the driver at fault. 

Claim the intersection? WTF is that? You go when you can safely do so and try to avoid the other idiot

Neither of you. Drivers making a left turn only have the right of way if they have a green left turn arrow.

I can see that English is not you best subject.  "... to claim the intersection when turning left on a solid green light..." means you are allowed to ENTER the intersection.  You do not EXIT the intersection until and unless all other traffic has cleared your path.

Your BIG mistake is "... the light was amber and I had to rush through the red light.... "  You don't CARE about the damn lights once you have entered the intersection.  Read the law -- the lights are about before entering the intersection.

Your  BIGGEST mistake is "Who has the right of way?"

The answer is NO ONE.  NO ONE ever ** has ** the right of way.

The "right of way" is always about who you YIELD to. 

Once you have entered the intersection, that big green light mean others car ram you -- they do not get to start moving until you finish your left turn.

That depends Anonymous...are you asking about a country that drives on the right, or left side of the road?

What did your instructor say when you asked him/her this question?

ALL traffic continuing straight through a traffic light in both directions that have the solid green have the right of way.

Anyone turning with a solid green light has to WAIT until the traffic from the opposite direction has cleared out.

Your instructor is a moron.

You don't "claim" the intersection on a solid green light when turning left. You yield to oncoming traffic going straight and turn left in front of oncoming traffic also turning to their left.