I think it is the older that you get but you would never know that platonic relationships are possible if TV and popular media are a daily part of your routine because they make it out to seem that sex is rampant and a necessity at all ages and demographics. I bet Cultures that put less emphasis on TV and popular media have more platonic, healthier, richer and productive relationships.

If you want a platonic relationship your best bet is to come out at the beginning and tell the other person exactly what you're looking for or what you want (no sex before marriage, etc.). We're programmed to be very visual and you have to fight that sometimes to get to the better stuff inside other people. That's why some people turn to Religion for help.