Picard saw how hard Jellico was to get along with first hand, and he also saw Jellico's negative reaction to Riker, but he defended him. In that one episode the master strategist says Riker is too "jovial" in command and Picard responds that he's a fool to question Riker's abilities. I'm guessing Picard doesn't like Jellico much either.
I'm surprised at the idea that Riker should have volunteered without being asked. All his previous recommendations to Jellico got him nowhere.