Unlike private lessons, skating school curricula have sets of skills at each level that you must master in order to pass to the next level.
In the USFS Basic Skills curriculum, each level contains testable skills that are critical for the next level (backwards one foot glides at Basic 4 before backward cross overs at Basic 5, for instance). The ISI curriculum contains all necessary skills for the "macro" skills within a single level, but the principal remains the same--you have to have the building skills before you can acquire the macro skills.
So what if a skater is missing "just one skill." Do you pass them on an "average?" Do you let it go?
ISI PreAlpha, Basic 1, 2, and 3 contain more or less only "building" skills, and no "macro" skills: forward and backward two foot and one foot glides, and marching or "push-and-glide" (weight shift from one foot to the other while moving forward), swizzles, one-foot pumps, forward to backwards two-foot turn, scooter pushes on a circle. I think everyone would agree that the ability to move forward on the ice and generate a two-foot glide is pretty basic, and that a skater that can't do this shouldn't move on.
But what about that one-foot glide? What if a kid does it really well on one foot but not at all on the other? This is the most common problem with kids on the cusp in these beginner levels. Well, next level, Alpha or Basic 4, is forward cross overs in both directions. If you can't balance on one foot, how are you going to cross? The building skill is necessary for the macro skill. I hate having to waste time in Alpha 1 class (much less Alpha 2) teaching kids this skill that they were supposed to master in the beginning level.
The next macro skill is backwards stroking and crossovers. Basic 3 and 4 include backwards one foot glides; again, this is necessary to the completion of a cross over, even the unfortunate swizzling ones that they allow in Basic Skills (snark snark This is the biggest problem with Basic Skills- USFS makes fun of the "ISI crossovers" with a lift, but ISI kids understand the weight shift in a backwards crossover better in my opinion. /digression). A good ISI teacher (that would be me) adds this Basic Skills skill into Beta class- gliding backwards on a circle.
How about t-stops? T-stops are stupid, and why do we have to do it in both directions? Well, that's essentially your hip/foot position for the mohawk turn in Gamma. Can't hold the "T"? You're gonna have trouble with the mohawk.
Both curricula are constructed to lead to later skills--proper bunny hops lead to proper waltz jumps which lead to proper axels. Proper understanding of 3-turns, equally strong in both directions, with the free hip held back, will make back 3s at FS4 or FreeSkate 1, and brackets at FS5 much easier. If you enter your ballet jump or mazurka with your toe pick facing forwards, you'll have difficulty learning a proper toe loop, and you'll never get the double.
Especially in the lower levels (which I count as thru FS3), every skill must be at minimum passing level, and preferably better. The more time you take with the basics, the easier time you'll have with the higher levels. A lot of my kids go through Alpha or Beta or Gamma 2 or 3 or even 4 times, but very few of them spend more than one session in FS2 or 3, because their basics are strong.
It's not just one skill. It's the bottom of the pyramid, and it needs to hold the whole structure up.