Not only everything He did, but everything He said was without sin. It was necessary that the Messiah be perfect so that He could redeem us from our sin. The Mosaic law is dear to the Jewish people, especially the more orthodox in practice. It is the heart and soul of religious Judaism. The problem is that no individual can possibly keep the law.
Perfect fulfillment is required.
This escapes the ability of everyone. The law is an instrument of God to show individuals that they have sinned and cannot keep God's perfect standards. Passages such as Deuteronomy 28 delineate this for the nation of Israel. For individuals, however, it is a concern of eternal destiny. After Adam sinned, all mankind inherited his sin nature.