In the question both batteries are connected in parallel with both positive on one side and negetive on the other side. So they are not opposing each other but helping each other and sharing the load equally. From fig-1 it is clear that potential difference across the resistor is 1V. So the current through it is 1A. This current will be shared by both batteries equally. ie 0.5A each.
Now suppose the circuit is like given in fig-2. Here the battery positive and negetive are opposing each other and the pd across the resistor becomes zero and so no current.
If the batteries are connected in series as shown in fig-3, we all know current will be 2A.