I'm not sure why the explanations weren't made more simple. Say you have 12v12 V batteries with 50 amp hours.
When you connect the batteries in series, say, 12v+12v then you get 24 volts at 50 ahAh When you connect the batteries in parallel, say 50ah50 Ah + 50ah you get 100ah100 Ah at 12v12 V.
If it isn't obvious as to what's happening yet, 24v24 V is pushing twice the amount of amperage "force". Therefore, it is why it "seems" only half of the amp hours are used, but indeed you are pushing the amperage with twice the force of 12v12 V.