In November 2000, a study was published by the Department of Veterinary Clinical Sciences, Graduate School of Veterinary Medicine, Hokkaido University, Sapporo, Japan and entitled 'Hematologic changes associated with the appearance of eccentrocytes after intragastric administration of garlic extract to dogs'.
Ever since then, the conclusion of the study has been copied and pasted 10,000+ times, such that it has obtained 'web truth' status, simply because everybody says so.
In layman's terms the findings state: When garlic is fed in very large amounts to dogs, it can cause oxidative damage to red blood cells, leading to a medical situation called Heinz body anemia.
However, if you take 10 minutes to analyse the figures, it very quickly becomes clear that giving garlic to dogs is only dangerous due to the massive doses administered during the study and shows that a dog weighing 10 lbs needs to eat 25 grams of garlic – about half an entire head of garlic (or about 6 to 8 cloves) every meal to experience any adverse effects. That really is a massive quantity.
This article from Dr Deva Khalsa, an holistic veterinary and teacher of veterinary medicine, explains in great detail why garlic is, in fact, GOOD for dogs in measured doses: http://www.dogsnaturallymagazine.com/garlic-friend-or-foe/
Here is the link to the original November 2000 study: https://www.ncbi.nlm.nih.gov/pubmed/11108195