I won second try with hares on medium, I think the trick is to:
A) make sure you get at least one hare to one of the central two spots (will always be possible) and camp it there. Keep your other hare moving around on your side.
B) the opponent will have to bring two hounds over to catch your other hare. To do this they will have to create a gap between the first and second hound in the middle spot above/below your camped hare. As soon as this happens, move your camped hare upwards.
It's pretty easy after that TBH. The AI has usual burnt a load of moves by that point and you have so many options from that position
The symmetry is restored if you say you're playing a two game match and the winner is the one that survives longer as the hares. But the game seems simple enough that I imagine it shouldn't be too hard to play optimally.
I beat both on hard fairly easily? Came back to comments expecting remarks on the shape of the board allowing for fairly easy "I just move back an forth as a hare" and "I just wait for you to move wrong as a hound"
As hares, if you rush one of the middle nodes, the hound machine could capture, but it never figured out moving two hounds all the way over to do so in my play. As hounds, it's basically the same, you just make sure none of the hares ever get "behind" you because then it's a lot harder to contain them.
Maybe the concept of desiring balance is modern. Maybe they wanted to encode asymmetry in the game to mirror nature, or the Master / Slave dynamic which they likely considered to be a natural law.