Spiritually speaking, does our society over-encourage us to procreate?

Its called free choice and I admire your question. You are fortunate in that you obviously come from a culture where you are even allowed to think your question let alone raise it on the web. In many cultures peoples lives are laid out before them, for good or bad, to repeat the problems ad infinitum. As you get older you views on what matters in life will change. Now perhaps you want to save the world, get a career etc. In years to come you hopefully will realise that the career thing is absolute baloney and perhaps having children is a good thing. However currently the population increasing at the expense of the environement suggests that we need a few more like minded people as yourself. Obviously humankind needs to replace itself to a certain level if we are to survive but the breed like rabbits and constant expansion thing supported by modern economics is one day going to backfire. Unfortunately its going to backfire very slowly so we dont really know we are doing it. Enjoy your life responsibly and you can't do any better than that.