Maybe they are looking at a Geneva flight that is not direct but is cheaper than Zurich.
As for disadvantages, if you are meeting a tour that starts in Zurich, it may be no disadvantage at all if you want to see a bit of Switzerland that is not included on the tour.
I personally have no interest in staying in Geneva; it is a big city and a center for many international organizations and multi-national corporations, but heavy on very expensive hotels and light on tourist attractions. However, the direct IC trains between Geneva Airport and Zurich offer some interesting stops that would make nice overnights. One goes along the lake as far as Morges, a charming small town with Audrey Hepburn connections, before passing through Neuchâtel, Biel, and other towns on the way to Zurich. We spent a night in Morges in a lakefront hotel before flying out of Geneva on one of our Swiss trips, and it was very enjoyable.
Another IC train goes by way of Lausanne, Fribourg, and Bern, any one of which might make. Nice overnight stop, although we have no personal experience with any so cannot make recommendations.
In other words, you can get off the plane in Geneva and take a train right from the airport to any of these places, some in an hour or less.