What's the meaning of "scar on the first cut"?

The answer to your question is given in your summary of the chapter:

Don't create a policy because one person did something wrong once.Policies are only meant for situations that come up over and over again.

Perhaps you meant to ask "Why does Jason Fried think unnecessary policies are like scar tissue"?

Not having read the book, I would suggest it is because as concisely described on http://activerecoveryboston.com

Scar tissue binds up and ties down tissues that need to move freely.

In terms of a business, time and energy can be tied up in complying with unnecessary policies set up to prevent a one-off situation from occurring again and this prevents the business from operating effectively.