I'm not saying he can push any animal. He goes in to detail with this in the New 52 series which people seem to like, though I can't understand why. He can do it fish because they are too primitive to know otherwise. Dolphins/Whales etc recognise him as their king.
That's it. They are the only animals he can control. Primitive life like fish and those under his dominion.
But he can induce seizures in people because a portion of our brain was inherited from fish.
Just because you don't like it doesn't make it gone. I'd include it because it's friggin' awesome. For me, their is no such thing as overpowered. Stories like All-Star Superman, Lucifer, Sandman, JLA, Grant Morrison's Batman and Mark Waid's Flash are amazing.