If you have your cellular data turned off due to being on wifi, or have a poor cellular signal, you cannot send picture messages. Also having cellular data turned off prevents you from receiving picture messages.
That is probably the problem then. I have my cellular Internet turned off because my phone ate through 65%+ of my data at random a week or so ago, and I haven't had it back on since. That you need the cellular Internet for it is kind of dumb, in my opinion.