First of all, its completely natural for Katniss to be hard to relate to- how could you???? Odds are, you've never been starving and forced to raise your whole family at a young age (actually, that's why I loved reading Mark Reads the Hunger Games, he was able to give me insight to that part of the story that was beyond my experiences). In addition, you can't apply ANY of our conventions to how Katniss is. Let's start with her being emotionally cold. Jodie was right that Katniss did NOT see love in her future. She didn't want to be a mother and have to worry about her children in the reaping. In addition, all Katniss has seen of love is from her parents, and her father's death destroyed her mother. A mother that Katniss has zero respect for. So even before Peeta comes into the story, we know that Katniss has love on the very bottom of her priority list- Gale is the closest she has to romantic love, and she's just too young to know what to do with it anyway.
Next, enter Peeta. You have to remember that although WE love Peeta, Katniss doesn't trust him at ALL. Don't forget that there is a huge class divide even within District 12. Peeta is other- he has a much better perceived life according to Katniss. She partially resents him even though Gale is more vocal about disliking the slightly wealthier/better fed. Even when it's clear to us that Peeta's feelings are genuine, she only sees his own means of survival- using her just as she is using him. There's no room for love.
Next, Katniss is FORCED to be with Peeta. Even if he is great and wonderful, it was the ONE decision she thought she could make for herself. Wouldn't you be a little resistant too if the man you hate picked your future husband? Especially when your best friend has suddenly started showing interest in you? Wouldn't you want the choice??
Then in the next books- Katniss is flat out suffering from Post Tramatic Stress Disorder. I read some reviews that applauded the author for handling PTSD really well- I think one review was the wife of a retired military guy and she saw a lot of the symptoms that Katniss displays when he got home- especially in book three. I would give Katniss a little more leeway when talking about her emotional growth- she's damaged. Severely. I think its most clear how far her and Peeta have come in the Epi- she has everything she wants and is trying to think of way to tell her kids her story- and how they still struggle years later.
I LOVED these books. Maybe there is no great message like in HP (love and friendship will get you through). It just the extremes of humanity- the most selfish, hateful, vicious, oblivious, callous, power hungry, and violent. It would be boring, I think, if Katniss were perfectly selfless and pure (that's Peeta's role in the story- which is why is hijacking is so shocking) but she tries. She struggles to stay retain her humanity amidst everything and I think it's incredibly powerful.