First off, let him. You only want guys who are dedicated to your fraternity. If they are questioning quitting during their pledge period, chances are they will not become the brother you envision. The sad reality of the situation is if you begging him to stay, you would just be postponing the inevitable.
However, you should take the opportunity to learn from this situation. The pledge is quitting because he doesn’t believe your fraternity is one worth joining. This is a huge red flag and needs to be investigated.
There could be a bunch of reasons why he doesn’t feel your fraternity isn’t worth joining. Maybe he doesn’t see the benefit of his financial commitment. Maybe he is sick of being hazed during his pledge period. Maybe the fraternity doesn’t have the robust social program he thought when he signed his bid. Maybe he simply doesn’t like the brothers.
Regardless, it is imperative that someone sit down with the pledge and have a candid talk with him. It might take a little bit of effort to pull the real reason out of him, but it will definitely be worth the time.
The brotherhood needs to take a hard look in the mirror once they find out the reason why the pledge wants to quit. The pledge has brought awareness to an issue the fraternity has, and now it is up to the fraternity to see if they want to change.
I understand that every fraternity has a lot of time and money invested in recruiting each pledge. Letting them go may seem like the worst thing in the world. I assure you it isn’t though. The worst thing in the world would be having a chapter full of brothers who are questioning their allegiance to the fraternity. That would be a real problem.