Bluetooth is a method of sending data from one device to another. The format of the data, even the data itself, isn't specified - so some devices will pair and transfer, some will pair but not transfer and some won't even pair. We're years from full Bluetooth compatibility. (It took years before you could send a picture by MMS from one carrier to another.)
However ... I suspect that your phone itself is defective. Pairing and using a speaker or headset is usually available in all Bluetooth devices.