I just don't get it. Everything I try, I lose.  If this is what the site is all about, I am not interested in going forward.  I don't want to fight anything, just want to raise, breed, sell beautiful creatures and admire them in my keep.

Besides, it's impossible to counter what they do since I am the one going first. Therefore there's no bloody way to win.  After 10-15 tries, I'm throwing in the towel.  Unless someone has a proven way to win. I don't see any cheat sheets on how to.  I want easy-peasy games; not head-scratching "huh?" games.

Just keep trying, 10-15 losses is pretty unlucky for the tutorial battle. 1-3 tries for a win is more normal, since the computer just does moves at random. The countermove system is virtually rock paper scissors... So what happened to you was almost like losing rock paper scissors 10-15 times in a row.

After the tutorial you can just explore for exp and completely ignore the battle area if you want. Doesn't change anything about the game.

Really though. The game isn't just about battling.. It's important for levelling.. but you can level pets by exploring, crafting, and quests... You don't need to just battle other users. Heck I rarely do it...

In time you will breed pets with wonderful genes that will make battling a breeze. Find pets that have Gladiator, Regeneration, or Second Breath (or similar genes) and good stats/genes, and high hitpoints. Make sure your mode of attack is with the method best for your pet.

But there are lots of things that you can do on the site that don't involve battling.

Also, since the game is still in beta, premium is free - this lets you do battles in automatic mode. This works so that in explore, you move your pet onto a monster and win or lose. There is no selecting maneuvers that may just be blocked, the game does it all for you. So, in essence once you are past the tutorial when you go explore on islands, just skip higher level monsters (you see their level by hovering over them) and fight the lower ones. This will level your pet up easily. 

And as Nightingale said, you will get much better pets than your starter pets. WIth those, it will be easy to go through the islands and fight (almost) everything you see. 

Don't give up yet =)