Which phone? Is this in the default text messaging app or is it in a chat app (like WhatsApp or Facebook Messenger)?
The Samsung Galaxy S9 offers a setting that disables the sending of read receipts, and this is how I access it:
Open Messages
Tap the three-dots menu in the upper right of the app, then tap Settings
Tap More settings
Tap Multimedia messages
Turn off the "Delivery reports" and "Read reports" toggles
You should be able to find similar settings by hunting around in your preferred messaging app.
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