For a long time I was getting captchas when posting links in Facebook due to Miranda NG. Then I switched to the development branch so I could use the SkypeWeb plugin and ran into even worse problems.
Since then, the problem has been fixed. I have been using the Facebook plugin for over a month and I'm not getting any captcha requests on Facebook.
If you still don't want to use it, consider Pidgin with the purple-facebook plugin. It is different, using the protocol used by Facebook Messenger instead of the web interface.