An unlikely Game of Thrones duo to end up together was Sansa Stark and Tyrion Lannister, but end up together they did. Shunted to a lesser member of the family after her engagement to Joffrey Lannister — er, Baratheon — broke apart, Sansa wasn't particularly happy about the choice. But Tyrion and Sansa had an odd understanding, and he was at least far more caring than his nephew.
Just because they had an understanding, doesn't mean that they were necessarily true friends though.
Sansa Felt Pressured
Sansa felt pressured by Tyrion to consummate their marriage, despite his insistence they didn't have to because he was aware it wouldn't be right. Despite his understanding approach, there was little doubt that Sansa still felt that weighing on her, as it was what was — unfairly — expected of her as a woman married to a nobleman in Westeros. It wasn't Tyrion's fault that these standards existed, but surely made her a little resentful of him.
She Just Wanted To Go Home
Sansa didn't want any attachments in King's Landing, even if it was one that was kind to her. By that point, she was dreaming of the North and it was the only place she wanted to be — back in Winterfell with what family she had left, away from the Lannisters. Tyrion might have been willing to be a friend to her, but Sansa just wanted her Northern friends.
The Age Difference
A more surface-level problem with their friendship? The age gap.
Especially in the books, Sansa was very young. Tyrion was an older man and there wasn't much in of life experience that they could relate to. Tyrion might have benefitted from having a friend his own age — like Bronn — and if Sansa needed a friend, a young woman might have been ideal.
That's not to say that friends of different ages are impossible, but they create a unique set of circumstances, and those just didn't mesh in this time of intense stress and high walls.
Sansa Wouldn't Open Up
Porcelain, ivory, steel.
Sansa described her transformation in the books very aptly, and she was at least on 'ivory' by this point. Her walls weren't coming down, they were going up, shutting her off from the world to protect her. There was no way she was willing to sit down and open up to someone, not just because of how much she was missing the North but she knew it wasn't safe.
Tyrion Perhaps Felt Judged By Her
Tyrion was always self-conscious of his size, something his father judged him harshly for, and he surely felt this way with Sansa too — who had hoped to marry someone far more conventionally handsome. Although her younger self might have definitely judged him, she had other problems by this point, but Tyrion certainly felt a bit defensive about her being forced to marry him.
Joffrey Made Them Afraid To Confide In Each Other
Even if the two of them had wanted to confide in each other, Joffrey made them too afraid.
People in King's Landing had a way of finding out things, particularly the powerful ones. No doubt if someone overheard Tyrion or Sansa venting, they would have reported back to Joffrey and the consequences would have been severe. They knew it was best to keep their mouths shut.
They Never Really Stood Up For Each Other
Actually, Tyrion stood up for Sansa when he felt it necessary — such as stopping Joffrey from having Meryn Trant beat her in the throne room. But for the most part, neither of them felt ionately enough about the other to defend them, especially when Joffrey was tormenting them.
Real friends stand up for each other, right?
Lannisters & Starks Can Never Really Be Friends
Their families and houses were probably a big factor in why they weren't friends, though. The Lannisters and Starks were completely at odds by that point, and Sansa wasn't willing to trust a Lannister because of all they had done to her family — Ned, Robb, Catelyn. Of course, this wasn't personally Tyrion's fault, but who could blame her for the association?
Tyrion Took The Fall For A Crime She Might Have Committed
No one ever found out who killed Joffrey, and it wasn't Sansa — but many suspected it. Nevertheless, Tyrion took the fall for her crime.
Neither of them tried to defend the other — it was every person for themselves after the king was killed and in such a serious matter, it's hard to blame them — but another sign they were hardly real friends. Just two people in the same predicament trying to make it out alive.
They Were Almost Just Too Similar
Ultimately, they were never real friends because they were just too similar. Both victims of cruel circumstances (mostly at the hands of the Lannisters), they were insecure, afraid, and their defense mechanisms were so high that they could no longer confide in anyone or open up. Sansa especially had completely gone into survival mode by the time they married, and that doesn't leave much room for others.