[throwup238]

Energy. Creating a single anti-hydrogen atom requires an absurd amount of energy to first create a collision in a particle accelerator and then capture that anti-hydrogen before it eliminates against another atom.

Only about 0.01% of the energy used to operate the particle collider creates antimatter, the vast majority of which is impossible to capture. All in all, the efficiency of the entire process - if you were to measure it in the e^2=(pc)^2+(mc^2)^2 sense - is probably on the order of 1e-9 or worse.

[mlindner]

Has there been research on more efficient ways to generate antiprotons? (By the way anti-hydrogen isn't how you would store it as anti-hydrogen can't be trapped.)

[fsh]

Anti-hydrogen is routinely trapped in magnetic traps at CERN.

[kadoban]

If anyone is curious how, I think this is vaguely the idea: https://alpha.web.cern.ch/science/2-trapping-antihydrogen

tl;dr: strong magnetic fields in a certain configuration since in a strong enough field anti-hydrogen acts like little bar magnets.