There's lots of media on the topic. Just pick and choose whatever argument suits you best. From the UFOpaedia information in Apocalypse, we can determine that the mind control process operates on two major factors. The first is the physical occupation of the parasite. All we know is the brainsucker is used to inject the parasite, so that it can directly attack the host from within and seize control. The parasite would have an advantage when it comes to flooding the victim with any sort of chemical to control and weaken his resolve. The second is the psionic aspect, which XCOM discovers very late in the war. This allows the parasite complete control over the host's consciousness, memories and actions. Killing the parasite outright probably wouldn't cure the mind control, because the agent has already been brainwashed by psionics. Likewise curing the psionic brainwashing won't do anything if the parasite is there to reassert control or simply kill the host. Curing the infection isn't part of XCOM's agenda. Their job is to stop the invasion entirely. That sort of cleanup would be left to the larger organizations like Nutrivend.