It's because Kishi's a terrible writer. I mean...really? Sakura's supposed to be one of the smarter characters in the damn manga, but the way Kishi writes her...she seems pretty dumb sometimes...
If this were real life...would Sasuke REALLY be worth the sheer amount of BS he's put those two through? Would he really be allowed back into the village just because Naruto wants everyone to just 'forgive' Sasuke for his crimes? No! The amount of stupidity going into that idea is just...I'd rip my hair out if it happened. That would be the BIGGEST bull sh*t move I've ever seen in fiction writing.
Have you by chance read Wuthering Heights, Jane Eyre, or The Count of Monte Cristo? All three of them, in their own way, contain story elements that you would probably consider a "sheer amount of BS" for the characters to be put through -- by another character or each other.
For example, take Wuthering Heights. Here's a portion of the synopsis from Wikipedia:
Catherine confesses to Nelly that Edgar proposed, that she accepted, and that this is despite the fact that she does not love Edgar—she loves Heathcliff, but cannot marry him because of his low social status and lack of education. She hopes to use her position as Edgar's wife to raise Heathcliff's standing. Heathcliff overhears this, and in despair he runs away and disappears without a trace. Distraught by Heathcliff's departure, Catherine makes herself ill out of spite. Nelly and Edgar thus begin to pander to her every whim to prevent her from becoming ill again. Three years pass, Edgar and Catherine marry, and live together at Thrushcross Grange.
Six months later, Heathcliff returns, now a wealthy gentleman. Catherine is delighted; Edgar is not. Edgar's sister, Isabella, soon falls in love with Heathcliff, who despises her but encourages the infatuation as a means of revenge. One day, he embraces Isabella, leading to an argument with Edgar. Upset, Catherine locks herself in her room, and begins to make herself ill again through spite and jealousy.
Likewise, in Jane Eyre, Edward Rochester is often viewed as sadistic and manipulative, torturing Jane with his relationship with Blanche Ingraham in order to make Jane jealous instead of admitting his true feelings -- all the while he is hiding an insane wife in the shuttered turret.
And The Count of Monte Cristo goes beyond a "sheer amount of BS" and is instead a vortex of emotional torture and vengeful dipshittery that the characters endure or impose on each other.
Considering that all three of these novels are considered classics of English literature and often make the top 100 novels of all time, I don't think Kishimoto is all that far off the mark, and his portrayal of romance and loyalty certainly doesn't make him a "terrible writer."
A reader has to remember not to judge the material by their own modern morality or personal standards. The world is full of people who would do things -- for good and bad -- that you would never do, but that doesn't make it stupid or unrealistic. Just different.
Besides, the "sheer amount of BS" concept is not unique to Naruto and Sakura and their relationship with Sasuke. Jiraiya spent a lifetime following Orochimaru because he never gave up on him; the Third struggled to kill him as well, regardless of what he did. Kakashi has lived with survivor's guilt, torment, and self-loathing his entire life because of his bond with Obito and Rin. Etc., etc.
Within the framework of the Naruto universe morality -- the ninja code -- taking friendship and team bonds very seriously, never giving up on your comrades, and doing everything in your power to help them stay on the right path is part of their lives.
It's not something that we as readers can judge by our personal ethics or experiences. If that were the case, I would totally agree. It's frustrating. I would have kicked Sasuke's butt to the curb a long time ago and never looked back. But I'm not a ninja.
It is love, it's Kishi's poorly written portrayal of love. One thing I will say though, is that she came pretty close to giving up on Sasuke during the summit arc. Attempting to kill him was her way of "saving" him, while on the other hand it's just a cop-out because she can't bare to see Sasuke sink further into the darkness.
I think it's worth remembering that Sakura never said any of that, it was purely speculation by Sai. We never saw Sakura form those words or thoughts. Sai isn't always correct when he interprets Sakura's behavior.
Even though NS will (most likely) be canon at this point I'm gonna have a hard time believing she loves Naruto as much if not more than Sauce because of the whole deal with her loving him so much she couldn't even put him down like a dog.
Naruto can't bring himself to put Sasuke down either. I guess that means he's in love with Sasuke too, right? 
Just a quick reminder guys: manga writers don't want their audience to have to over-think everything. It would be a little strange to write something that is meant to wear out people's minds with what-ifs.
Very true.
