Several reasons.
1) It looks terrible. Only 4 coaches have been fired like that in D-I football in over a decade. We're not an SEC heavy hitter and we can't get away with that.
2) Because then they'd have to appoint an interim coach. The players are still behind Brew. There is a better chance of player disenchantment if Brew is straight up gone. MSU did the "fire but let him coach it out" plan with John L Smith and as far as I can tell the transition was pretty smooth. If anything, the players might try to put him out on a high note as much as possible.
I thought about this a little more and wanted to expand on my thoughts. This is what I just posted over at The Daily Gopher (apologize for the parts that are sort of repetitive).
1) Only about 4 coaches have been canned mid-season in D-1 football in over a decade. I’m pretty sure it was Fuller who put that in an article after the NIU game. No link only because I can’t find it (and I don’t blame anyone who doesn’t believe me b/c my memory is not perfect). We’re not an SEC powerhouse. It looks bad in the coaching community if we fire a guy midseason b/c that just isn’t done.
2) Personally, I think its more likely that the players pack it in when given an interim coach to play for. They still seem to be behind Brew (he is a player’s coach) and while I’m sure some will be disappointed that he’s being let go, it gives them another reason to play hard for the guy the rest of the way. Plus, both Horton is the “new guy”. I’m sure they like him, but I doubt they know him as well as Brew. Same is sort of true for Cosgrove, but I doubt he would want the responsibility given what his family is going through. And lets face it, the kids aren’t dumb. They can probably see the writing on the wall too so what harm is there in getting the news out of the way?
3) Recruiting. It takes away the uncertainty in one way and adds it in another. We’re screwed either way, but at least recruits will know they have a new guy coming.
4) Hiring process. This gives them the benefits of a full firing (they can be open about forming a search committee, other coaches know the job is open) without the problems of #1 and #2.
5) Fans are relieved either way. There will be some yokels who keep calling for his head, but for rational fans this will be cathartic just like a full firing without the problems of #1 and #2.