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Doing so requires MMS.

MMS requires both the following:

• Settings > Messages > MMS Messaging = "On"
• Your cellular carrier must allow MMS on your plan. This may cost extra.

Especially if you're using text.

I guess "Messenger" might mean Facebook Messenger, which has absolutely nothing to do with the statements above.

Yes, this does sound like a carrier issue.

Good luck, and enjoy your iPhone.