If people can't retweet you, than it can be happened because of two reasons only. First is your account on private and second there may be an existing setting in your account that disallows retweeting. If you want to allow retweeting than adhere below steps:
• Log in to your twitter a/c
• On the top right, simply click on your name and choose ‘settings’
• Go to the ‘Tweet privacy’ box and uncheck it
• Click the ‘save’ button at bottom
It will discover your tweets posts and people can re-tweet its.