I use wifi and was told when I called Verizon that you need to have mobile and wifi on to text. Why? All my other phones the wifi worked. I don't understand.
Welcome to Android Central! If you want to send and receive MMS (i.e., picture messages), you need mobile data on, since that's how MMS is sent. But for simple SMS, you don't need either, since SMS goes over the voice signal.
If you have your SMS (texting) app set to not break up long texts (or to send long texts as MMS - different apps word it differently but it means the same thing) you need mobile data or wifi on to send the MMS that results. If you have it set to break up long texts (or not send them as MMS), it sends long texts as a series of 160 character texts (that's the longest single SMS you can send) and he receiving app pastes them together as a single text. And you don't need wifi or mobile data.