My guess is that because Alex Jones exposed some real weird shit (bilderberg meetings, satanic rituals etc.) in his early years and he was never taken serious he kinda started believing in his own conspiracy theories.
Still, in a world that has Iraq invaded under false pretenses and stuff like the Tunkin Gulf Incident and Reichstag fires his 'ravings' don't seem all that crazy in a 'even a broken clock is right, once a day' kind of way.
He especially fits perfectly into the post-truth world we find ourselves in today. People also don't give him enough credit for being able to talk without prepared remarks and offer detailed explanations for 4.5 hours.
Somehow his fat little brain stores everything from the history of Nazi's to the names of Mayan gods.