Combat is turn-based and there is no time limit on each round in a PVE Pet Battle. You can take your time to determine which spell to use next. Some pet abilities have multiple round cooldowns, while others can do extra damage if certain conditions are met. Be creative and have fun testing which combination of attacks works best against different wild pets!
Analogy: think back on riding the swings in kindergarten. Was it fun? Now, imagine going back to those swings exactly as they were, and sitting in them now, as an adult. They're too small. They don't fit. Your feet drag on the ground because they're so low to the ground. The bar over your head is low enough that you can reach out and touch it, and even at the highest the swing will go, it's only about chest high when you're standing up. It's exactly the same swing, but riding on it now is a very different experience, yes?
With the Classic beta now out it seems every related article somehow manages to spark the eternal war of "Vanilla was the best WoW sucks now" and "lol nostalgia goggles, Vanilla sucked, enjoy your two weeks of Classic". I have to say, even though I understand the principles behind the battle and the reasons people behave and talk this way... I actually REALLY don't get it on a deeper level.