Why does my data plan need to be on to send pictures with text? I don't understand why data is needed to send a picture with a text or to send a text to multiple recipients. These things did not need data on a dumb phone. They just used texting.
Assuming you're speaking about the Short Message Service: For sending pictures without text, that's done via a special "signal channel", where exactly 160 bytes fit into a single package (hence the limit of 160 chars). But when you want to include more (more text, multi-media elements like pictures or video, or some other attachments), those "additional data" don't fit into this "package" – so your message is switched to MMS.

Other than SMS, MMS are sent and received via mobile data (often via a special Access Point configured in your device). So this is the reason why it requires your data plan to send "pictures with text": you basically switch to a different service. Details can be found behind the links, if needed.