The more than 30-year-long debate about soccer heading is well-chronicled in Webbe's 2010 Handbook of Sports Neuropsychology.  It began in the early 1980's with studies by Alf Tysvaer and his colleagues of retired Norwegian professional soccer players which reported abnormal EEG findings and other neurological, cervical spine, and neuropsychological difficulties. [8-12]
Tysvaer's findings were dismissed at the time as being due to a combination of the fact that the players were using old, heavy balls and their known predilection to drink alcohol. After a study appeared in 1990  that supported Tysvaer's findings, with results that could not be explained away by the type of ball used, a "spate of studies ensued," writes Webbe, "some of which supported findings of neurocognitive impairment in soccer players and some of which did not."
Significantly, however, it was during this period that the "most controversial of Tysvaer's findings" - that neurocognitive deficits were correlated with lifetime frequency of heading soccer balls - received additional support, setting the stage, Webbe says, "for years of confrontational rhetoric over whether heading was causative in neurocognitive impairment" in which the science and politics of soccer intertwined.
The soccer community, he said, resisted reports that suggested difficulty regarding heading, even in the face of growing concern among the scientific community and the media, not just about concussions in soccer, but the risk of brain injury from repetitive heading, with even the scientists becoming embroiled in the controversy; some maintaining that soccer heading had the potential for harm and some saying it didn't.
On one side, Webbe says, is what he loosely refers to as the "soccer establishment," consisting of FIFA, the United States Soccer Federation, England's Football Association (FA), and the various groups advising them. Studies that reported on heading-related concerns and impairment among players were, he says, "dismissed in almost a knee-jerk reaction" by these groups, with heading becoming essentially a "sacred cow within some segments of the soccer establishment." When peer-reviewed, objectively well-done studies showed adverse outcomes of heading, [6,14,15] the soccer establishment discounted them in favor of other studies that showed no effects or relationships. [16-18]
But, as Webbe notes, it wasn't just soccer governing bodies that reacted "defensively and aggressively" to studies showing that heading may be systematically injurious to players; many soccer aficionados, players, coaches, parents, and even scientists also, he says, "discounted the science, arguing against some decent studies that heading was a perfectly safe practice." 
In addition to the political controversy, Webbe says, the disparity in scientific outcomes - with many studies by capable researchers reporting no relationship between soccer heading and neurocognitive impairment and a "different set of studies by equally capable authors using similar methodologies and similar tests to the first set f[inding] significant relationships between the cumulative and/or seasonal amount of heading and neurocognitive deficits," are difficult to reconcile.
A comprehensive meta-analysis in 2003  identified several methodological issues that the authors said explained the false positive findings, chief among them the fact that many of studies relied upon self-report of the players - which numerous studies have found to be problematic in terms of reliability and validity - while only a very few [4,8] used direct observation.
Recent findings from a pilot study of retired professional English soccer players  found that, once their playing careers end, the chronic low-level head trauma they sustained from repetitive heading did not put them at greater risk of long-term cognitive decline than the general population, but, as with many of the other studies, that study has since been criticized (by Webbe, among others) as being methodologically flawed. Several other recent studies using formal cognitive testing - neither cited in the SLI White Paper - have also failed to detect changes with ball heading in young adults,  or in 13- to 16-year-old soccer players.
A number of recent studies, however, point in the other direction. In a 2013 study  cited in the SLI White Paper, researchers at the Albert Einstein College of Medicine, using an advanced imaging technique called Diffusion Tensor Imaging or DTI, linked frequent heading of a soccer ball with changes to the white matter of the brain and poorer performance on a neurocognitive test of memory in adult amateur soccer payers who had been playing the sport for many years. Their findings suggested that there may be a heading threshold above which the risk of short- and possibly long-term brain injury dramatically increases.
Similar findings were also obtained in another recent imaging study (also cited by the SLI White Paper) which found differences in white matter integrity in a small sample of young (e.g. 20 year old) professional male soccer players who had played since childhood, as compared with a control group of swimmers roughly the same age.
In another 2013 study,  researchers at the University of Texas found that frequent sub-concussive heading caused at least short term cognitive dysfunction in a small sample of female high school soccer players tested right after practice which was consistent with mild traumatic brain injury to the frontal lobe of the brain. The researchers found that the cognitive impairment was marginally related to the number of headed balls, but significantly related to hours of soccer per week and years playing soccer.
The study was cited by the SLI White Paper as adding to the "growing body of evidence showing that heading a soccer ball can result in problems with memory and attention, as well as structural and metabolic differences on advanced brain imaging, even in the absence of a symptomatic concussion." But, as Webbe notes, left out of the White Paper is any mention of the fact that the research was a pilot study involving only 12 subjects, did not explain the nature of the heading that occurred during practice, and did not make a comparison to a control group of soccer players who practiced, but did not head.
The SLI White Paper also implies that the cognitive dysfunction the players experienced was long-term, but the authors of the University of Texas study were careful to point out that the "most conservative interpretation of our findings is that these changes are transient and the result of the immediately preceding soccer session," and to state that, without additional data, they preferred that more conservative interpretation.