The sword signifies killing. In Genesis 3 the killing of the sword indicates God's righteousness (cf. Lam. 3:42-43; Rom. 2:5). If God would kill someone without sin being involved, He could be condemned for acting unjustly. However, since sin was involved, there is, according to the righteous God, the need for killing. Hence, the sword for killing signifies the requirements of God's righteousness. Therefore, God's glory, holiness, and righteousness closed the way to the tree of life, indicating that man, as long as he was sinful, was not permitted to contact God as the tree of life.
Now we need to consider two illustrations of God's closing the way to the tree of life. On Mount Sinai God came to visit His people (Exo. 19:10—20:21). However, He seemed to say to Moses, "Moses, tell the people that I must have a boundary around the mountain and that none of them should cross over the boundary. I am holy, righteous, and full of glory. None of you sinful persons are qualified to step over that boundary. If you do, you will die." Mount Sinai was covered with a cloud in which was the glory of God (Exo. 24:16-17). That glory was very demanding. It separated all sinful people from the presence of God and it closed the way to the tree of life. Also, on the mount was the consuming fire (Exo. 19:18). The Israelites were so terrified that they said to Moses, "Oh, don't ask us to go to God. You approach Him for us. Look what is on the mountain—the devouring fire. We dare not go one step further." That was the requirement of God's holiness. Furthermore, during His meeting with Moses on Mount Sinai God gave the law, the ten righteous commandments (Exo. 20:1-17). Those commandments also were very demanding. Thus, on Mount Sinai we see a picture of three items: the glory of God, the holiness of God, and the righteousness of God. These divine attributes placed demands and requirements upon sinful man. Hence, man was kept away from God as the tree of life by God's glory, holiness, and righteousness.
A second illustration is the tabernacle in the center of which was the Holiest of all (Lev. 16:1-2). God was in the holiest place, and His shekinah glory continually filled it. However, no man could enter the holiest place at any time, because the cherubim which were over the ark (Exo. 25:18-20) were watching whether or not sinful man could fulfill the righteous requirements of God. This meant that the glory of God was there observing. Also, cherubim were embroidered on the separating veil (Exo. 26:31-34). Furthermore, when the two sons of Aaron, Nadab and Abihu, went into the holy place with strange fire, they were burned to death (Lev. 10:1-3). Fire, indicating God's holiness, came out of the holiest place to devour them. Moreover, in the ark in the Holiest of all was the law of God (Exo. 40:20-21; Heb. 9:3-4). The law signified God's righteousness. Therefore, once again we see that the glory, the holiness, and the righteousness of God made demands upon sinful man and prevented him from contacting God.