Live photos only send as still photos iPhone SE

Brand new iPhone SE. My iMessage recipients all have up-to-date iOS. I took a few "Live" photos, but when I try to send via iMessage, they go as still photos only. In fact, I can see before I send that the photo isn't "Live". I am not using settings for enabling low quality photos. I have done a Settings Reset. Nothing is working to let me send a Live photo.

My previous iPhone was a 5S, so I couldn't even TAKE Live photos. But I could view them from iMessage senders. This is very frustrating.