I think the important thing to realize here, and Scaedwian is trying to help you understand, is that "ground" or "zero volts", and "positive" vs "negative" is a human conceived point of reference whose meaning is derived literally only when connected to an "Earth ground" circuit. A transformer isolates the circuit on the secondary side from any and all ground references, unless of course the designer chooses to establish another ground by tapping the secondary. This is what a center tapped power supply does with respect to Mains AC, at least in North American electronics. A recent thread here actually helped me realize a misunderstanding concerning transmission line power and transformers.
So, in your circuit everything is floating because it is battery powered. The secondary is an AC waveform, not much different than what an AC generator produces. The cycle of current is sinusoidal, so the oscillation is a 360 degree cycle that mimics the mechanical rotation of the generator rotor converting magnetic energy to electrical. A polarized magnetic body in rotation has two poles, "north" and "south" or "+" and "-", and in a full cycle these poles will pass the neutral point where their influence is balanced TWICE. With that neutral point as a reference, we can establish our zero volt or "ground" point for all the electrically connected circuits afterward. However, any currents induced through a transformer beyond the source will be floating.
This is basically what your circuit is doing, on the primary side you have an oscillator creating this waveform, inducing it through a transformer. In a free floating AC waveform such as you are creating, we can consider the neutral point where polarity change is 90 degrees from either extreme to be zero volts, with, in your case, 6 volts swing to the positive and 6 volts to the negative, for a total of 12 volts.