Try it with read & write then test again!
Also, an interesting place to look at would be https://ask.cyberthana.com/logs and /admin/logs to know exactly what is failing.
Also, Your forum seems to be configured over SSL so one thing to check will be force_https in your admin panel and confirming if you have set up https links in the twitter application.
My twitter configuration is as follows and it works fine:
Settings to request email and App permission is Read only.
refer this: