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actually, the answer is a lot more simple than you guys make it out to be. Think about how you take off regular...the key to your spin is the carve. take a look at guys like lolo and andreas- they carve so hard thats why their big spins looks waaay better than most.
The likelihood is that you cant carve switch very well. If you naturally spin left, then taking off switch spinning left is going to mean your turn will be initiated by the inside of your left knee...now think about it...when you take off regular, to spin left, the carve is initiated by the inside of your right knee.
This is where the discrepancy lies, and also why a lot of people find it easier to spin the opposite direction switch - because the carve is coming from your 'weaker' or less used side. this is why more advanced and pro skiiers dont have this problem, because they dont have a weaker side generally speaking.
So the answer to your problem is to work on the strength of your weaker side, in the gym and on the slopes. That means, really practise your right turns when skiing regular, and your left turns when skiing switch. Also focus on the support leg, because its more than likely that this is acting as a counter to your turns if it is indeed much stronger
Good luck guys