So which argument are we actually discussing here? Because in the OPs post and in yours there are two different arguments that, for whatever reason, are bundled together and used as a motte and bailey.

Argument #1: Certain kids are privileged enough to be able to afford tutoring and get into good schools and this is unfair to the poor kids

Argument #2: Certain kids are being pushed UNNECESSARILY by their parents to participate in a rat race when their time would be better suited to doing something else

I think those are two sides of the same argument.

If certain kids are getting in because of tutoring rather than because of talent/ability, then they are the kids that are being pushed unnecessarily to participate when they'd be better off doing something else. Those kids take up the space of kids who are poor who could benefit from that kind of instruction.