The actual problem is that you haven’t accurately defined the core elements of your business. The solution here is to only consider outsourcing those functions that don’t require interaction with customers. You need to reexamine your definition of what your core function is. I’d urge you to consider any area of your business in which you deal with customers or clients as the core of your business. Without customers and clients you have nothing. They are your most precious resource.
While it’s the outsourcing firm’s job to get you to trust them, getting your clients or customers to trust you remains one of your most important tasks. There’s no need to turn this no around. If you’ve made a mistake in defining your core business, simply start over with a new definition.
I’ll lose quality control.
This is also entirely rational believe me, I know firsthand. Make sure you’ve done a top-notch job of researching, interviewing, and checking up on all the candidate firms. Carefully go over exactly what services each will provide and the procedures they’ll follow. Look for steps in the process when you will have a chance to check up on their work. Query their other clients or customers.
Ironically, this is a problem where you don’t want to have too much trust in another party. Explain that while you trust the firm to do a good job, you need to have some oversight role in the process. Say that you’re not looking to control them, only to keep a watchful eye on the bottom line. You may want to hint that the level of your oversight could diminish over time as you become more comfortable with them. Also, insist on their conducting internal oversight as well. Remember, the person who brings you into their company may concentrate only on marketing.