You have not correctly linked your Mojang and Twitch.tv accounts, please link your accounts here and then relogin to the launcher.
Requirements for streaming: Windows: Vista/7/8 (32 or 64bit) and Mac: 10.8/10.9 (64bit only).
Windows XP is not supported by Twitch.tv and it is recommended you upgrade your operating system as Microsoft will be dropping support for XP on April 08, 2014.
Linux streaming is currently unsupported as the appropriate Java libraries have not been released by Twitch.tv at this time.
OpenGL 1.5 is also currently required for Twitch.tv streaming, if you have not please update graphics card drivers here or obtain a newer video card with the minimum requirements. If you do not know if your card meets minimum requirements, for technical support please use the Mojang Support Center.