Given her family being Yang/Fire/Heaven based an engagement against her interests is particularly odd though. The combo says the family bloodline is hotblooded, and prone to going My Way, Damn The Costs(much like a Wind based clan is going to have cohesion issues because there'd be a tendency to resolve disputes by moving the disputing parties away from each other). Given Fan Yu's own level of ability, she's a pretty damned poor match, which is unlikely to improve political relations so much as put it into a pressure cooker(since political matches usually are predicated upon them being at worst unenthusiatic on both sides).
I think we're missing a major component of the scenario here(which Xiulan is hardly going to expose her family's internal matters even to a good friend).
My gut says it might well be to distance her from a Han Jian pairing than to actually promote a Fan family pairing, but thats possibly an unreliable reading due to his lack of presence in Ling Qi's PoV. Early Xiulan was pretty aggressive in her pursuit of Han Jian after all.
I think the biggest components you're missing here is the attitude and time factors.
Xiulan actually has a pretty mercenary attitude to marriage unless it involves her. Remember how she responded to Ling Qi's being uncomfortable with Huang Da's rapey attention with 'the Huang are a pretty high status family and you're a commoner. Why aren't you happy?'.
From what she's said about being ordered to introduce us to her cousins, as well as Gu Tai's remarks about the Gu being very traditional when we brought up how uncomfortable we were with jumping into a marriage with someone we've met for 5 minutes I think we can assume this is a fairly widely held attitude within the clan, and certainly the view of its current leader. So generally they think of an arranged marriage as a duty of a noble, which means Clan members generally aren't likely to be fiercely opposed to political marriages even with their volatile temperaments.
Coming on the heels of this is what
@Arkeus said about status. IIRC the Fan are on par with or slightly below Han Jian's family, who are the second highest rank of nobility, just below dukes (Marquis?). By contrast the Gu are significantly lower status, being a vassal family to the Han. We see from Xiulan's earlier comments that marrying into a higher staus family is a big deal and something the Gu really want.
Next is time/age. Xiulan is 14, so is Fan Yu. Going into this year it might easily have been felt that whilst Xiulan didn't like him she didn't absolutely despise him. Given Fan Yu's obvious infatuation there was a decent possiblity that she'd warm up to him, especially if/when Han Jian finally got up the bottle to reject Xiulan. I mean if we look at the early updates we see that Xiulan's attitude to commoners isn't actually that different from Fan Yu's sneering condesencion.
Also in that vein there is the talent issue. Before the year began I do not believe it was realised/obvious how big the talent differential between Fan Yu and his fiance was, with them starting the year roughly on par. Frankly whilst I'm still not sure she'd like him I do think part of the issue Xiulan has had with him as the year goes on is how little he has advanced, which was not an easily predicted factor when the contract was signed.
I think (if I recall correctly) Xiulan's significant cultivation (and speed) advantage over Fan Yu was being used to press for more advantages to the Gu side of the contract, but was not (yet) enough to justify breaking the engagement or pressing for a different husband from the Fan.
Finally there is the issue of cultivation growth and its effect on her personality. As Xiulan's cultivation has grown the distortion of her personality towards her elements has as well, and I suspect she was not the most calm person to begin with. Add the tribulation, which I think has exacabated Xiulan's already strongly fire natured personality to new heights, and made her even more impulsive and willful and locking in attitudes far sooner than might be expected even from a Gu.
But again if we consider the idea I mentioned earlier that their families might have thought they'd warm up to each other, or at least not have her dislike Fan Yu the way she does this may have never become an issue.
