Garlic contains a chemical called allyl cysteine sulphoxide or ‘alliin’. When a raw garlic clove is crushed or chopped, an enzyme in the garlic cells is released that reacts in a matter of seconds with the alliin to produce a chemical called allicin. This breaks down into lots of other chemicals, most of them stinky.
Nearly all of these chemicals are broken down in your stomach and liver, but allyl methyl sulphide is one that survives to be absorbed into the bloodstream intact. This means that it can diffuse out through your lungs into the air you exhale for up to two days. Brushing your teeth has only limited effect because the chemical is still in your blood.