Howdy Nislija,
It sounds as if you are having an issue with turning off Find My iPhone for your iPhone when doing so from the iPhone itself.
There are some other methods you can use to turn off Find My iPhone, described in this article - iCloud: Remove your device from Find My iPhone
Specifically -
If you can’t turn off Find My iPhone on the device, turn off the device so it goes offline, then remove it from Find My iPhone on iCloud.com.
You can also remove your iOS device by first erasing it—just follow the instructions below for removing an iOS device you don’t have. You can later restore the device from an iCloud or iTunes backup.
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Turn off the device you want to remove.
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Go to Find My iPhone on iCloud.com on another computer.
If you’re using another iCloud app, click the app’s name at the top of the iCloud.com window, then click Find My iPhone.
If you don’t see Find My iPhone on iCloud.com, your account just has access to iCloud web-only features. To gain access to other iCloud features, set up iCloud on your iOS device or Mac.
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Click All Devices, select the offline device, then click Remove from Account. If you don’t see Remove from Account, click All Devices again, then click the Delete button next to the device.
If the device comes online again, it reappears in Find My iPhone. If your device reappears, turn off Find My iPhone on the device (follow the instructions above for removing a device by turning off Find My iPhone), or if it’s an iOS device and you no longer have it, follow the instructions below for removing an iOS device you no longer have.
Thanks for using Apple Support Communities.
Best to you.