I can see why this is confusing as usually there would be a purpose implied.
Can you just accept that with 'grow up' we say all sorts of things but it doesn't mean that was the purpose for the child growing up? for example - he grew up to become an alcoholic. I don't think you'd believe the child's whole purpose was to become an alcoholic.
In any case - no-one grows up just to achieve one thing. A child who wanted to grow up to become an Olympic athlete isn't going to say 'oh I'm never going to make it, I'll just kill myself as that was the only reason I had for growing up.'
There is no causality here as there is in your shop example. I want to buy something - therefore I go to the shop. yes. I want to be an Olympic champion - therefore I'll grow up. No.