What is the intuitive reason why matter and antimatter should be highly reactive? Common knowledge has it that when an amount of matter and an amount of antimatter come anywhere near each other, they annihilate, leaving nothing but "pure energy". 
In more technical terms, maybe we could say that a particle-antiparticle annihilation has a very high cross-section, and the products have all quantum numbers equal to zero. As pointed out in the comments, for the high cross-section we should probably restrict to annihilation due to strong or electromagnetic interactions.
My question is about the high cross-section. Thinking about the factors influencing the cross-section (especially in QED), we see


*

*the number of vertices in the Feynman diagrams involved: the lowest level would just have a single vertex, so that is OK. (Let's ignore that to ensure conservation of momentum this cannot really stand by itself).

*the mass of the exchange particle: no propagators.

*the availability of final states.


At least the first two are clearly favorable for a relatively high cross-section, but it is not clear that it would be exceptionally high compared to other elementary interactions.
Is the last one an important contributor? Is there some other contributor that I overlooked? Or is the cross-section not actually that exceptionally high compared to other processes?
 A: It's just not true that particle-antiparticle interactions have particularly large cross-sections, even if it is "common knowledge".
On the timescale of human perception, objects made of protons will immediately react with objects made of antiprotons that touch them. But that's not special to antiprotons. The same would be true for another object made of protons, which is part of why you can't put your hand through a wall. This is simply because humans react amazingly slowly compared to any nuclear timescales. We only treat the particle-antiparticle reaction as more salient because it's more violent.
At the level of cross-sections for high-energy particle collisions, there's no particular reason to favor particle-antiparticle reactions. For example, some past colliders used proton and antiproton beams, while the LHC only uses proton beams. In both cases, most of the time most of the stuff in the beams just passes through each other. You can compute the cross-sections directly, and they are comparable. 
