Haters gonna hate, but Paramore and Fall Out Boy make great rock music. Any band that gained notoriety during the post-pop-punk-emo boom of the mid-2000s has been pigeonholed into a very specific category -- namely, much of the general public doesn't consider them to be credible rock and roll.
Fall Out Boy has certainly experienced a great deal of this backlash, despite continuing to mature as a group and output good music. Many of the bands of that era could not grow past it; Paramore and Fall Out Boy, who are co-headlining this summer's MONUMENTOUR, are both talented exceptions. Touring together was a wise and logical choice.