Here is a more specific example of why Gil's initial advice is good advice.
I am rebuilding Mich St in Wooden, B+ prestige. Had locked up to front court players with minimal effort, and I show up on a guard the same cycle as Kentucky (A prestige). I get about 30-35k in (I had 4 schollies, and a total budget of about 65 - 70k), and realize there is no way for me to win the battle, and Kentucky realizes this too. He decides he isnt going to spend anymore unless needed, so now I have a guard that I am dead in the water on showing on my list, I have wasted half my budget on, and is showing as "struggling between" on WOTS, despite there being literally zero chance he comes to Mich St.
I need to move on to other targest, and if I leave him on my list, my new battles might be more inclined to battle me if they can see him and it looks like I am battling Kentucky. Instead, I offer the redshirt, pull his schooly, he is off my list, and now I only have the other 2 players on my list, both showing "not 100% sold" to Mich St, and to someone looking at my list the first time, it looks like I have the majority of my budget left, when in reality I have spent well over half.
I was able to move in on 2 other guards where I'd have the advantage in the situation, but realistically would have lost had I been battled, but I didnt get battled because I looked stronger than I really was, and I think that is the point Gil is making.
By leaving "battles" on your list that you arent really in, you are giving away your position by either showing how weak you are, or making yourself look weaker than you are. "Struggling" could mean each school has 5k in or 30k in, and it's up to the other guys to determine that. I almost always bail on guys when I am beat. And plus, you can always reoffer the scholly and pull the redshirt and get almost all of that effort back if you want to jump back in later.