So, the question presupposes a grander purpose than whatever your parents were trying to achieve
No, I don't think it does. When you are in a prison, and you ask your cellmate, "why are we here?" that begs the answer: because somebody else put us here. The reason, however, that the question begs that answer, is because you and the person you are speaking to understand the full context of the prison, and more importantly, understand how that environment relates to reality
outside of said environment.
If you suddenly found yourself in a room from which there was no escape, you might be able to infer how you got there from seeing others forcibly put in similar rooms. However, if the explanation for why
they were forcing people into confined spaces was because they were forced to do so by others who were themselves forced to do so, that would not neccesarily beg the answer "I am here for a grander pupose."
There are three purposes served by your being in the prison.
Well, the analogy clearly fails here, because if I allowed myself to get arrested and put in to prison for my own benefit, say, because i intended to help facilitate my accomplice's jailbreak, or because i was homeless, hungry, and needed healthcare, then the question "why am I here?" could be relevantly addressed by saying "I am here because of my own motives."
If we assume that the person who has put you here for some end is a good person - and I think they demonstrably are, but for now let's just assume it -
Okay, I will assume it- but i expect you to demonstrate it at some point or that leaves a pretty large gaping hole in your argument.
then we can safely assume that the end for which we have been put here is a good one.
Only assuming the person that put you here is able, which you haven't demonstrated.
Why on earth would a good person put innocent people in it?
I can think of some reasons. 1. To contain and control the wrongdoers (think prison guards) 2. To rehabilitate the wrongdoers. 3. Because "innocence" implies a lack of wrongdoing, which typically implies that there is wrong doing to be done. You mentioned that "You did wrong of your own free will" which implies that at some point the wrondoers were innocent.
So, those who ask "what is the purpose of us being here?" already assume a divine purpose.
No, not neccesarily. To be alive is to do. At the most basic level, your body "does" keep you alive by pumping blood, processing nutrients, bringing oxygen to your blood cells, etc. That's without you conciously "doing" anything. When you "do" things, you assume a purpose. To eat is to keep yourself alive, even if you don't
conciously intend to. When you eat because you're hungry, you are, at least on a subconcious level, eating to quench a desire. A desire has a purpose, namely to propell you towards an end.
All these things are quite easily recognizable, but when you ask, what's
life's purpose, you can't really give a reasonable answer other than "to create more life." However, when we begin to abstract, and ask " what's the purpose of that?" We go down a seemingly never ending road, because one can always ask "whats the purpose of purpose?"
So, at some point, one wishes to have a purpose that ties all the other ones together. But just because one wishes, does not gurantee that one will get. If there is a purpose that ties all purposes together, than either it will be unobtainable, or obtainable. If unobtainable, than one might ask "what's the purpose of my pursuing this unobtainable purpose?" But if obtainable, one might ask "what is the purpose of obtaining this purpose, since i will then have no more purpose?"
In conclusion, existence does
not beg a divine purpose, neither does the question "why am i here?" Just because the question cannot be reasonably answered does not imply a transcendent, divine answer. That simply exchanges one mystery for another.