The rough explanation I've heard before is to satisfy conservation of momentum and energy together. But on doing some more digging this seems wrong. C12+gamma is an output, just only for 0.01% of reactions. No idea why the different byproducts have different rates though.
> Why would the carbon split? Why not stay carbon?
Don't know — I'm not knowledgeable enough in this area to do more than take WAGs about it. The sequence might be different: For example, the 1H proton might not ever fuse with the 5B11 to form 6C12; instead, the fusion reaction might be that the 5B11 fissions into two 2He4 and one tritium 1H3, after which the 1H proton fuses to the tritium to form the third 2He4.
> And wouldn't this technically be fission energy then?