The metallic interface between insulating LaAlO3 and SrTiO3 opens up the field of oxide electronics. With more than a decade of researches on this heterostructure, the origin of the interfacial conductivity, however, remains unsettled. Here we resolve this long-standing puzzle by atomic-scale observation of electron-gas formation for screening hidden lattice instabilities, rejuvenated near the interface by epitaxial strain. Using atomic-resolution imaging and electron spectroscopy, the generally accepted notions of polar catastrophe and cation intermixing for the metallic interface are discounted. Instead, the conductivity onset at the critical thickness of 4-unit cell LaAlO3 on SrTiO3 substrate is accompanied with head-to-head ferroelectric-like polarizations across the interface due to strain-rejuvenated ferroelectric-like instabilities in the materials. The divergent depolarization fields of the head-to-head polarizations cast the interface into an electron reservoir, forming screening electron gas in SrTiO3 with LaAlO3 hosting complementary localized holes. The ferroelectric-like polarizations and electron-hole juxtaposition reveal the cooperative nature of metallic LaAlO3/SrTiO3.