We investigate the collisional quenching of cold metastable antiprotonic atomcules [(p) over bar He+], by HZ molecules in view of the recent state-resolved measurements at CERN. Firstly, we determine ab initio the 6-D intermolecular interaction between the four (anti)nuclei at the CCSD(T)/CP level. After averaging the interaction over the fast (p) over bar orbits, we exhibit reactive channels and activation barriers below few 100 muE(h). Hence, we account qualitatively for the order of magnitude and (n,l) dependence of the quenching cross-sections measured at 30 K, after estimating tunneling probabilities. We also account for the lower quenching efficiency by deuterium. However improving this overall agreement would require the determination of numerous finer contributions. We monitor the saturation of electronic correlation with larger basis sets; we estimate the importance of dynamical relaxation effects; and we stress the role of quantum vibrational and rotational delocalization for the light (p, (p) over bar) nuclei. The latter vibrational corrections lower the barriers, while the rotational H-2 averaging defavours isotropic para-H-2 (J = 0). As a result, we mainly attribute the quenching at 30 K to ortho-H-2 (J = 1). Additional experiments at other temperatures and with para-H-2 would further constrain this orthopara quenching selectivity, and provide an ideal four-body benchmark for further chemical physics investigations (including tunneling effects, collision-induced Auger decay, etc). (C) 2002 Elsevier Science B.V. All rights reserved.