Answer: In order to get symmetry, we have to get to the point where only the poison square is left or there is one square open above the poison and one to the right, as below:
In order to get there, we need to maintain having one square more shaded in the top row than in the bottom row. Therefore, if the other player plays in the top row (red) you play in the bottom row (blue) (Figure 1) and if the other player plays in the bottom row (red), you play in the top row (blue) (Figure 2).
So as the first player, with a winning strategy, your first move should be to take the upper right corner so that you set up this pattern.