You're setting up your event and notice the option Is Private? under Event Setup > Settings > Event Basics. But what does this mean?
This feature doesn't limit who can sign up for an event but it does remove some opportunities for users to share the event with others. Once this setting is enabled, all of the social sharing buttons found on your public event site and any viral incentives you have set up will be disabled.
For example, after your attendees complete the checkout process, the social sharing option will not show up on the confirmation page.
They will also disappear from your session pages and speaker pages.
If you want to go a step further and also remove the tweet button found in the 'You're in!' email, head to Event Setup > Email Templates > Attendee Emails and click on the three dots (...) next to the email template and then Customize. Once you're there, click on the green tick next to the button. It should turn grey and the button will then appear faded on your screen. It will then no longer be included in this attendee email.
Note that this feature doesn't block someone from sharing a link to your event on social media of their own accord, but instead removes the instances found on an event site where sharing is by default encouraged.