The question's a good one--and, off the top of my head, I couldn't point to any concrete incentives on the part of Biscuit as to why Gon was elected to battle with Genthru. However, some glances at the material printed in volumes 15-18 go some way to illuminating possible motivations on the part of Gon's team--and further portrayals of the relationship between Gon and Killua with Biscuit in volume 20 assist in underscoring that it is perhaps Biscuit's mere modus operandi --her way of doing things--that gave birth to the battle between Gon and Genthru.
In the volumes following Biscuit's introduction, her character is portrayed as being unreasonable in her demands, an impression created not simply by the severity of the tasks that she demands Gon and Killua perform--digging to Masadora; sleeping with rocks dangling overhead--but because these painful demands are offset against the comparatively tame exercises that her student, Wing, had them perform previously. Her way of teaching is plainly brutal; it's almost antiquated--she's far older than Wing, so it's not too much of an imaginative leap to say that she believes in older, more disciplinarian ways of schooling people rather than the more contemporary and forgiving teachings of her student--which engenders an impression that she might be a little bit too demanding, and perhaps a little too expecting, of her pupils. Her methods are symbolic of bygone days when teachings were stricter and perhaps out of touch; these antediluvian methods of teaching are necessary in communicating Biscuit's persona as the archetypal old sage/sensei character that most shounen manga possess--it's an intentional quality, one that is instrumental in shaping Biscuit's reasoning for Gon doing battle with Genthru. Gon is often touted as being dead-set on his objectives--but it's worth bearing in mind that Biscuit is every bit as unflinching in her methods, proving unrelenting and no-nonsense in her approach; when Gon is tasked with perfecting his emission exercises in the latter half of volume 17, Biscuit recognises that his probability of success is low, yet she leaves the task up to him anyway, and it is very telling]that Togashi introduces Cookie the magical masseuse mere pages after she gives Gon this task. Cookie was used to heal Gon and expedite his training during the battle with Knuckle, and it could have done exactly the same here--yet she chooses not to heal him in this instance. Biscuit betrays signs here that she fosters some high expectations of Gon; her refusal to employ Cookie implies a stubborn belief in Gon and the rightness of her teachings that is later shown to be misplaced: he fails the task--Biscuit doesn't always get things right. Putting Gon in her place to fight Genthru was a gamble. She has her own reasons for wanting to win Greed Island--she wants Blue Planet, after all--so she does want victory over Genthru, but her instinctive nature to take risks means that she's content to weigh up the permutations that could--not certainly--give rise to victory which also indulge Gon and Killua's preferences. In volume 20, Biscuit explains to Killua that calculated odds of victory--predicated on the unlikely assumption of each competitor being at 100% capacity on the day of the fight--are undesirable traits to foster in battle; a weak opponent can still beat a stronger opponent on the stronger person's off-day; so although having her take on Genthru made the most sense from a tactical perspective, it is not a plan that marries well with her approach to combat and teaching. It's not all about percentages and likely-hoods for Biscuit--that was the way Killua operated, and she scolded him for this way of thinking. Biscuit's beliefs are those of experienced nen users--something made clear when Morel foreshadows her words in volume 19, when he states that you should always fight as if "you're 100% positive that you can win"--she recognises that so much is variable when combat is involved: gambling is something she would long have been used to if this approach to battle was a modus operandi she'd been espousing for long. At this stage, she wouldn't be averse to taking risks, suggesting that her belief in Gon is based on her own combat orthodoxy and life experiences. Hitherto, her teachings to Gon and Killua had largely been successful; from her perspective, a belief in Gon's abilities would logically not be misplaced. Even though his victory was not guaranteed, she acted as if she was, in Morel's words, "100% confident" that he would win; because her thinking as a nen-user would not permit her to consider his loss, Gon's victory was never in question for her after sufficient precautions had been taken. Ergo, there was no longer any profit to be gained from her fighting Genthru--in her eyes, victory was logically ensured whether it be her or Gon fighting--whereas much could be gained from letting Gon do the dirty work.
Biscuit's selection of Gon for the battle with Genthru may also have been based on psychological perspectives to battle. Following the dodge-ball game, Gon was the one to openly retort to Genthru when communications were opened through the binders. As an opponent, Genthru may potentially have been most expecting of Gon as his challenger when battle rolled around. Biscuit states in volume 17 that they--Gon's team--can't let Genthru know that they'd been preparing for battle the whole time. Were it the case that Biscuit was made to confront Genthru alone, Genthru could feasibly have questioned why it wasn't Gon, the one who so vehemently decried his methods, that chose to go up against him. Biscuit could perhaps have aroused too much suspicion--she wouldn't have been the natural choice--which would have been counter-productive in that Genthru would have erected some defence against her--perhaps even to the tune of rallying together his buddies against the unlikely threat, negating the one-on-one fighting style that Gon's team had been planning to create. Biscuit states during her fight with Bara, after revealing her true form, that one should "never show one's hand" in battle--something that having her fight against Genthru would have been, effectively. Pitting Gon against Genthru best created the circumstance for the latter to underestimate Gon; with Biscuit already shown to have a capacity for going for long-shots, she would've likely been happy enough with Gon's chances under these conditions. Objectively, Gon's chances look unreasonably low--a lot of the fight is plotted around educated guesses as to how Genthru will fight and respond--but Biscuit has been shown to make unreasonable demands of him in the past, such as requests for fighting with a "less than 1% margin of error", so this sort of match-up doesn't conflict with her beliefs as to what is reasonable to expect and stipulate. As identified in the opening post, Genthru more or less does flow with the educated guesses Gon's team made; Biscuit may well have evaluated that Genthru was a decent test for Gon, and such was her tendency to risk--and such was her lofty strength of belief--that she believed Gon could triumph.
Or maybe the whole reason for the Gon vs. Genthru fight was Yoshihiro Togashi simply trying to make the fight more interesting by creating the most desirable tournament match-ups in the way that earned him such renown in Yu Yu Hakusho!
