I found out why Yui's career choice was rejected. She made a mistake while filling in her form, writing down her career choice under her choice of university:
Left column reads 学校名: "School Name"
Middle column reads 学部名: "School Department"
Right Column reads: 学科・コース: "Course of Study"
So, CoalGuys' lack of typesetting is why hardly anyone picked up on this. I hope that Frostii does it right.