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I'm just about ready to give up, but I'll try and say this another way...
Assuming the inputs are perfectly balanced, then the output of each opamp will be 180 degrees opposed. If you took those two outputs and summed them together, there would be no signal, because they cancel each other, yes?
Now, if the transformer was replaced with 2 5k resistors in series, and you fed the output of the opamps (180 degress opposed) into each end of this network, what would you see at the centre tap of the two resistors? It's a summing point, yes?
Transformers are impedance convertors, so in reality, with a 10k load and 1:1 ratio, the primary looks like 2 5k resistors in series with a grounded "no signal" (voltage wise) centre tap with respect to the 180 degrees opposed signals. If the signals were in phase, it's a different story.
It's exactly the same as driving a loudspeaker coil with a bridged power amplifier.
There is nothing mystical about it.
Tim.
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