what certain skills would i miss out on moving to a larger bike?
You inadvertently answered your own question.
Skills are learned thru practice, making mistakes, etc. If your riding a super sport (600cc sport bike) its going to be VERY sensitive to throttle input, braking etc. Not a good combination for a learner.
Two outcomes.
1) You over ride your skill and end up sliding across the pavement.
2) You baby the bike around to avoid the above....and end up learning little to nothing.
There is a reason that most of the professional riders have worked their way up thru the ranks....start on something appropriate, learn to ride it....and I mean REALLY ride it.....then upgrade after the bike is holding you back.
This doesnt mean put 500 miles on a Ninja 250 then you can go buy a Hyabusa.
A GOOD rider on a Ninja 250 will walk all over a rider on a 600 GSXR with poor skills.
To simplify.....a bike your afraid is going to kill you at any moment is NOT the bike you want to learn on.
You NEED to be able to accidentally drop the clutch and not have the bike rocket out from under you.......you need to be able to grab to much throttle and not have the bike slam you into the vehicle ahead of you.