Why is freshly-chopped garlic sticky?
When crushed or chopped, garlic releases mercaptins from within its cells (sulfur containing compounds). Sulfur readily forms bonds with other amino acids, notably cystine which itself contains a sulfur atom in its chemical structure. When two sulfhydryl groups (S-H) come into close proximity, a disulfide bridge can be formed, creating a relatively strong chemical bond between the two molecules. This chemical attraction between the proteins in you skin and the garlic compounds causes the sensation of stickiness, much like hydrolyzed sugar sticking to your skin. Since lipids (oils) have a stronger attraction to the oils that coat your skin, they displace the sulfurs and prevent your hands from being sticky.

When garlic is roasted, the proteins within are denatured (lose their function) and lead to a milder taste and less sticky chemicals.