Right now we're witnessing a technological race to mass adoption for cryptocurrencies. Any hit to a specific cryptocurrency means that a certain number of users will switch to the alternative goods. In these types of races (e.g. Iridium, Betamax, etc.) that means an eventual death.
While Bitcoin most likely won't be mass adopted because of liquidity issues, that doesn't mean another implementation of cryptocurrency won't be able to overcome that.
Certainly, a hurt that doesn't kill bitcoin doesn't make it stronger.
Economics apart, the protocol is a huge breakthrough.
The idea as applied to your example is that if the kid is pushed around day after day then maybe by the 100th day he'll realise the bullies don't have any _real_ power over him. He'll become resilient to their bullying. If he is smart he'll learn tactics to combat their bullying, be they by avoiding the bullies, talking to them or hitting the gym and learning martial arts. The saying is basically saying the longer you are exposed to setbacks the longer you have to overcome them.
In that regard, if the MtGox demise doesn't take out bitcoin completely the bitcoin that rises will be more wary of exchanges that cannot or will not prove their reserves. There have already been multiple ideas put forth for how this can be done and I think I even saw a post on HN with someone who claims to have implemented one of them.
That which doesn't make you stronger, kills you.
Which is equivalent, but more obviously absurd.
If a car runs me over and breaks something in my body, but I manage to survive, it doesn't make me stronger or car-crash resistant.
The original maxim is in the first person which seems to imply it should be considered an expression of a personal mantra (or indeed maxim) rather than an observation about people in general(which would be pretty dumb).
Related to bitcoin, of course if Russia, EU, JP, China, US, AU, Brazil and Turkey decide that it's illegal and should be stopped for the greater good, bitcoin with it's current form will either die or lose a huge % of it's current value.
I understand that it's good (and to me a little bit suspicious) to come clean and totally intact out of DPR bust and SK downfall, survive MtGox's failure, but ultimately if beaten too hard it's going to die not become stronger.