Okay, the way the turns work is this:
First - if you have the faster dino, you get the first hit in. With some dinos, you have priority abilities, which allow them to cloak, or evade before you can strike. If you have dinos like Tanycolagreus, which can nullify these, then all the better, since this means their evade or cloak will fail.
Second - a lot of stuns or crits are rolled by a Random Number Generator (or RNG for short). If you attack, the RNG calculates whether or not you made a successful stun or critical hit. Each dino has a certain percentage chance that these will work, however. Let’s say you have a dino with an attack that grants it a 30% chance to stun. If you attack with this ability, the AI uses the RNG to essentially “roll the dice”. If it comes up with equal to or greater than the 30%, you stun. If not, you don’t. This has caused a lot of ire in the community, especially because it all seems a bit off sometimes. But it’s all percentages in the end. Sometimes you get winning streaks, sometimes you get losing streaks.
Third, the moves all have a cooldown period before they can be used again. With certain dinos like the common raptor, it’s short. Pounce, strike, pounce. But with dinos possessing special moves, like Irritator or any of his spinosaur brethren, you have a cooldown between moves of more than one turn. (R2C isn’t really all that great, it gives you an additional % chance of a crit, but it leaves you open for attack)
Another thing: matchmaking. Matches are based on trophy count, not player level. So if you run into someone with dinos way more powerful than yours, it’s probably either because they were dropped by losing streaks in the tournament, or they deliberately lost trophies in order to drop down to lower arenas and collect DNA exclusive to those arenas. They just didn’t think to switch the dinos out on their team, or they’re just really inconsiderate.