A rocking motion when chopping garlic allows for more efficient mincing and helps to release more of the flavorful oils. This technique also reduces the risk of cutting yourself.
The rocking motion, typically used with a chef's knife, is superior for chopping garlic for several reasons. First, it allows you to keep the tip of the knife in contact with the cutting board at all times, increasing stability and control. This reduces the chance of the garlic cloves slipping out from under the blade, which can lead to uneven chopping and potential injury. Second, the rocking motion applies consistent pressure across the garlic, effectively crushing and mincing it. This crushing action ruptures more cells in the garlic, releasing allicin, the compound responsible for garlic's pungent flavor and aroma. Finally, the rocking motion is faster and more efficient than a simple up-and-down chopping motion, especially when dealing with multiple cloves. You can quickly mince a large quantity of garlic with minimal effort.
After mincing your garlic, add a pinch of salt to the pile and continue rocking the knife over it. The salt acts as an abrasive, further breaking down the garlic and creating a paste-like consistency that incorporates beautifully into sauces and dressings.