With Family Tree Builder version 7.0 or higher, a family tree that was created in Family Tree Builder has to be synced at least once with the family site, in order to become editable online.
Please read the following article for more details regarding edit permissions: How can I enable my site members to edit my family tree online?
Please note: if your tree was created in Family Tree Builder and published with the old version of the software (FTB 6.0 or older), it cannot be edited online. In this case you should download the latest version and sync your tree with the site. Then it will become editable online.
You can download the latest version of the Family Tree Builder software here.