There is no reason to travel to other worlds to mine rare earth metals though, we can do that on near earth asteroids and helium is the main element that we will have to mine in the near future. Thankfully Jupiter's atmosphere is basically 25% helium. No helium, no rockets, no mri, no chance and we're squandering it away thanks to congress. Once it gets out in the atmosphere it basically heads out into space to never be seen from again.
However the truth of the matter is that we will head into space because we want too. For the same reason people climb stupid ass tall mountains. If not that, then for survival. Those who may not be fond of the idea will do so for the same reason as always, money.