Answer:
It seems that either you were blocked, or you accidently blocked them.
Based on the messaging UI, you're on an iPhone, so to check blocked contacts, you can go to: Settings -> Messages -> Blocked Contacts;
If you see the contact in the list of blocked contacts, simply click the Edit button at the top right, and remove the contact from the blocked contact list.
If the contact is not blocked, then there may be something else wrong, perhaps with your service provided, or maybe on the end of the receiver.