Many have tried to simultaneously run their business and sell it at the same time. It usually ends in failure or at the very least an exhausting and confusing experience.
Look at it this way. For most owners, running their business is a full time job. A job you know well, one that you pretty much do on instinct fuelled by loads of experience. Your team has worked with you and each other for a reasonably long period of time. So decisions are made quickly. They are important and key to keeping the machine running smoothly. But they tend to revolve around you.
Selling a business is filled with unknowns. A process you're unfamiliar with. Add in new team members who you may not be comfortable with yet. There will be a requirement for decisions that you either don't have the experience with or the time to learn.
The questions, requests for documentation and meetings never end. Sleepless nights and a strain on your family life will add to the frustration.
It's like taking on a new job or project for a customer. One you are currently very unqualified for. You will need to go through a learning curve that you likely have no time for.
So why add this additional and very difficult job to your usual busy schedule? It's a recipe for disaster, or at the very least failure. It will almost certainly adversely impact your company. Do you really want to do this as a second job?
You and your business need to be in a place where the company runs without you. This is a good thing. If you want the best shot at selling, a Buyer wants to see that the company can run smoothly without you anyway. One day you will no longer be in the picture. The Buyer needs to believe this is realistic.