In the movies and in the books, why does Katniss (not in the sense of denying) never say she loves Peeta or make him feel that she loves him, not until the end of the last book?
Because she isn't sure.
After their first Games, they've been through a lot together, but they've had to pretend to be in love for the sake of the cameras. That's an excellent way to stop real love from forming, or to make people deny (even to themselves) whatever real feelings they may have. Quoting from the first book:
I don't know. I haven't even begun to separate out my feelings about Peeta. It's too complicated. What I did as part of the Games. As opposed to what I did out of anger at the Capitol. Or because of how it would be viewed back in District 12. Or simply because it was the only decent thing to do. Or what I did because I cared about him.
In their second Games, more or less the same is true, only she has enough genuine care and respect for him (she's not sure whether it's love) to want to save his life more than her own. She does start to have some kind of feelings for him then, but she's too unsure of her own mind to be able to share them with him. Perhaps her strongest feeling is when they kiss on the beach:
"No one really needs me," he says, and there's no self-pity in his voice. It's true his family doesn't need him. They will mourn him, as will a handful of friends. But they will get on. Even Haymitch, with the help of a lot of white liquor, will get on. I realize only one person will be damaged beyond repair if Peeta dies. Me.
"I do," I say. "I need you." He looks upset, takes a deep breath as if to begin a long argument, and that's no good, no good at all, because he'll start going on about Prim and my mother and everything and I'll just get confused. So before he can talk, I stop his lips with a kiss.
I feel that thing again. The thing I only felt once before. In the cave last year, when I was trying to get Haymitch to send us food. I kissed Peeta about a thousand times during those Games and after. But there was only one kiss that made me feel something stir deep inside. Only one that made me want more. But my head wound started bleeding and he made me lie down.
This time, there is nothing but us to interrupt us. And after a few attempts, Peeta gives up on talking. The sensation inside me grows warmer and spreads out from my chest, down through my body, out along my arms and legs, to the tips of my being. Instead of satisfying me, the kisses have the opposite effect, of making my need greater. I thought I was something of an expert on hunger, but this is an entirely new kind.
Remember also that throughout their Games (the main time they spend together, at least in what we see of them in the first two books), they're constantly on camera and displayed live to the whole of Panem. Not the best situation in which to declare any real feelings. The closest they get is in the scene I've just quoted.
In Mockingjay, the first time she sees him is when he's been hijacked into a 'mutt' to kill her - again, obviously not a situation in which she can declare her love. His rehabilitation process is long and slow, and by the time he's fully recovered, the war is over and they're back in District 12. And that's the time when she does eventually tell him she loves him:
"You love me. Real or not real?"
And I say, "Real."
Because she had feelings for both Peeta and Gale and therefore was unsure of her feelings throughout the series.
She was always close with Gale but her relationship with Peeta started out as an act to generate sympathy and sponsorship.
During the series she grows even closer to both Gale and Peeta. You could even say she loved both of them. However she rejects Gale in the end, in part because he
helped create the bombs that killed Prim.
So with Gale out of the picture, Katniss was much less confused about her feelings - she loved Peeta, and was then able to say it:
PEETA: You love me. Real or not real?
luckily for her, Peeta was still waiting around for her
In the book Mockingjay, when she realizes Snow is torturing Peeta because she's the Mockingjay, everyone tries to comfort her but she thinks:
In the end, the only person I truly want to comfort me is Haymitch, because he loves Peeta, too.
Basically admitting it without realizing.
She loves Peeta but she feels Gale will be hurt by her actions. It is not fair on both boys but it's not fair on her because they make her feel she has to choose between them...