(Spoilers Main) Why did the show flip Ned and Catelyn's motivations about Robert's offer of hand of the king?
In the book, Ned is the one who wants to refuse the offer whilst Catelyn is the one insisting he should take it. Ned's reasoning is that he likes it up north and has no desire to run the seven kingdoms down south in the capital, whilst Catelyn's reasoning is that she fears Robert would take the rejection poorly and begin viewing the Starks as enemies. Ned insists he and Robert are like brothers whilst Catelyn reminds him that he hasn't seen the king in over ten years. Then, upon hearing of Robert's additional offer to marry Joffrey to Sansa, Catelyn is further convinced that Ned should accept the king's offers since it would mean Sansa gets to be queen and thus make their family even more powerful and secure.
All this discussion is had with the backdrop of the dead stag/direwolf omen which fits into the theme about characters interpreting prophecy incorrectly. Catelyn thinks she needs to convince Ned to accept the king's offer since otherwise the king will view the rejection as an insult and eventually oppose their family which will bring about all of their destruction. However, it is actually the opposite. Rejecting the offer would've probably avoided the war of the five kings and saved their family and Westeros from so much destruction. A classic "prophecy will bite your prick off" moment that George loves to explore.
However in the show, it's the other way around. Ned feels obligated by duty and honor to accept the king's offer even though he doesn't want to, whilst Catelyn strongly encourages him to refuse the king so he and the family can keep living happily up in the north. The omen of the dead stag/direwolf now takes on new meaning as something the characters just didn't heed as opposed to misinterpreting.
Ultimately in both cases what convinces Ned to go south and accept the position is Lysa's letter accusing the Lannisters of poisoning Jon Arryn. Still, I'm not sure why the show changed things in the way that it did considering how inconsequential the alteration was for the larger plot.
Thoughts?