One of the primary concerns with halogen-free solder pastes and fluxes revolves around the wetting and coalescence. The reason that halogens (usually in the form of covalently bonded halides) are used in the flux is because they are very effective at oxide removal. The halogen-free alternatives just aren't as efficient.
So, what is head-in-pillow and what is the correlation to halogen-free? Head-in-pillow is an assembly defect in which the bumps from a BGA or CSP don't coalesce with the solder paste on the PCB pad. The root cause of this defect is typically from component warpage. However, there is experimental evidence that suggests that solder pastes with better activity (ability to remove oxides) are less prone to this defect. There is the link to halogen-free. If a halogen-free solder paste is not as effective at oxide removal, there is a potential for an increased occurance of this head-in-pillow defect.