1. It would piss off North Korea
2. It would piss off China
3. It would piss off Russia
4. It would piss off the UN
5. It would piss off US taxpayers who are footing the bill
Yet, in my mind, 1-4 (especially 4) are all reasons FOR arming Japan :)
Seriously, however, if I were to play devils advocate, the main argument that I would harp on is the resultant regional and international instability that may ensue.
It very well could reverse any progress that we've made in getting North Korea to surrender their nukes. It could cause China to accelerate their already massive and troubling build up of their Navy. Russia, who is already feeling paranoid about ex-Soviet states to their west embracing the US and EU, would become even more agitated if we were to arm a country that has been historically hostile to them.
All of this could lead to strained trade relations between four of the largest economic powers on the planet (US, Japan, China and Russia) -- which would act as an anchor on the world and US economies.
Juxtaposing these possible scenarios with the billions of dollars it would undoubtedly cost to give Japan cool military toys, one could make a cost-benefit analysis argument that it's just not in US overall nat'l security interests to have an armed Japan. Particularly when we still have bases IN that country that remain available to us if we ever feel we need to flex some military muscle in the region.
EDIT: I meant to preface all of this by assuming that all of this is contingent on the hypothetical situation of Japan changing the pacifist clause of their constitution. As it is currently, Japan can not constitutionally maintain a war-capable military presence. That's a significant obstacle to this scenario as most Japanese are vehemently pro-pacifist.