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It was impossible not to love the Doctor. Rose, Martha, Queen Elizabeth I, Madame de Pompadour, and one very persistent otter knew that very well. River knew it best.
She was not made to love, in fact, she was explicitly raised and taught to do the opposite - especially in the case of the Doctor. Despite not remembering most of her childhood, as it goes with trauma caused by violent psychological conditioning and constantly being around very-tall-but-well-dressed creatures you cannot remember, River was raised to hate the Doctor from birth.
Hate was an emotion that one simply could not feel for someone they don't know and who never hurt them, but River certainly wanted the man dead. His death meant freedom for her, and she'd sort of wanted to punish him for whatever he had done to make someone fear him so much that they created her. It was easy to blame him for her lot in life, especially when she learned of her parents.
Meeting her mother changed everything. Amy Pond was the kindest little girl River had ever met, but she had not met very many children in her life. Amy immediately claimed River as her friend when River 'transferred' to her school in year 9. River played the part, acting as Amy's friend. Somewhere along the way, acting was no longer needed - River genuinely liked her new friend.
Amy Pond met Melody a bit before River found out who her parents were. They were already close friends but Melody couldn't help but look at Amy differently. Amy noticed, because of course she had, and Melody was not sure how to explain away to awe in her eyes when she looked at her mother, her friend.
Then her father walked in.
He looked at Amy with awe in his eyes as well.
Melody hadn't met Rory yet, but she quickly grew to love him and Amy beyond words. They were her only safety and her only fun for years.
Rory was always there for Melody, helping her in school, teaching her how to drive (albeit against his will and in a stolen car), and even standing up against much bigger boys for her. Rory told her when she was wrong, but never thought less of her for it.
Amy taught Melody how to be a person, showed her what girlhood was. Amy would stand by Melody when she was wrong, especially when she was wrong. Amy made Melody feel normal.
It was impossible for Melody not to love her parents.
It was a foregone conclusion that they would love her back.
Part of River, the part that insisted she was unlovable and wrong, insisted that her parents felt some kind of biological urge to love her. That if they had met and Melody had not been their daughter that they would have the same distaste for her that everybody else always seemed to.
That part of her was quieted by the unabashed and forceful love she saw in the Doctor's eyes.
He had no obligation to love her, no reason to.
Loving River was his choice.
The Doctor had seen all of her, had understood her completely in a way that nobody else could, and he had loved her.
She was quite sure her love for him outshine his for her by several orders of magnitude, but it didn't matter. He loved her for whatever reason, and she would selfishly take every moment she could.
River and the Doctor were written in the stars, their mark made on every planet they saved together and everyone they met across time and space. She knew their time together was limited, knew that she would be left behind in the immense lifespan of the Doctor, but she was able to comfort herself when she looked out at a universe of stars that they had touched.
River knew the Doctor loved her, but never imagined how much until Darillium. Until he rewrote history and broke every rule of his people just to take her out to dinner at the most beautiful place she'd ever seen.
The Doctor had settled down with her. The Doctor, a man who ran and ran and never looked back, had spent years with her. He had bought them a house, had gotten a job, had done the impossible for her.
Together they had a domestic life, a normal life despite who they both were. Something she knew he had run from with everything in him before, but now he had initiated specifically for her. He'd given her something she hadn't even known she'd wanted, a normal life with him.
The Doctor hadn't saved her in the end, not in the way that mattered. She was saved to a mainframe, living in a literal dream, but it simply never matched her life with him.
Until the day it did. The Doctor finally came back for her.
He explained it as bigeneration, something that to her sounded like complete nonsense that he'd made up to come back for her. She had screamed and cried and hit him, thinking that he had died for her.
He had, but not in the way she thought. He was still out there, saving the universe. But he was also here, looking so tired, so much older than she had ever seen when she looked in his eyes.
At the end of his life, he came back for her. And together they were saved, both by a mainframe and their all encompassing and deep eternal love for each other.
Apparently, loving River was impossible for the Doctor not to do.