It wasn't so much the days of the week, it was, rather, the urgency of getting the interview done. School starts Monday (presumably). Paperwork was completed one week before school starts and apparently evaluated by Tuesday. Now I imagine that the interview needs to take place asap so that the process to get the student enrolled can get moving. At this point in the process, I would think that not only every day, but every hour would count in getting this process completed so that the student can sign up for classes and be able to start on Monday.
So yeah, maybe it could wait another day, maybe it could wait till Friday, I don't know. But it appears to me that in this case, if the student wants to be enrolled in time to start next week, the interview needs to get done quickly.
Anyway, that's what I'm assuming is going on here and why the OP only gave the student one day to respond. And again, the message was, if neither of these work, let's see what does.