We do exactly the same thing. We cover ourselves because we know that there are people in the world who will hurt us. Sometimes they hurt us because they are malicious and they are seeking to do us damage, but more often they are simply acting out of their own hurt and shame and we become incidental victims to the consequences of their sin. A teacher has had an argument with her husband before she leaves for work in the morning and her students get an extra helping of stern-and-demanding all day. Your boss dresses you down and you kick the dog on the way in the front door. It's almost a cliche.
But there's a deeper level to all this. First, notice that the fig leaves are an attempt to cover, to deny, our sin. But our nakedness is not our sin. We think our vulnerability is the problem and we try to "fix" it. So we build walls around our vulnerability. We promise ourselves we won't ever let anybody get close enough to hurt us in that particularly tender spot. We deny that tenderness even exists in us. If anyone or anything gets too close, we close off and wall up and walk away. Nothing to see here, folks. After a while we start to believe the lie that we don't feel, don't hurt, don't care, don't love. It's all rooted in a hurt and vulnerability we'd just as soon deny. This is so often the story behind a married couple who say, "We just don't love each other any more -- there's no point in keeping up this sham." They head for divorce court thinking next time they'll get it right, but the root issue -- the fear of wounding, the fig leaves over their unresolved vulnerability -- is still there and it destroys the second marriage, and the third.
The other part of this -- and we don't like looking in this mirror -- is that our disobedience to God hurts other people. Because our walls, our inner vows, our determination to avoid pain, are all disobedience to God who says, "Come to me and I will give you rest" (see Matthew 11:28-30) and "I am the Lord who heals you" (Exodus 15:26). We decide to cover and protect ourselves -- and as we deal with our own wounds, everyone within range gets to share our pain. We don't like to admit it, but most of the wounds we inflict are involuntary. We don't want to cause pain, but my friend's saying is true of us -- "Hurt people hurt people."
Instinctively we know that our sin needs to be covered. That is true. But instead of going to God in repentance (which is very different from shame) we patch together leaves and make an ineffective suit that cuts us off from others and from God. We spend our time rearranging the leaves, patching the holes, and our attention is taken from a God-given focus outward -- love -- and we turn inward, concerned about ourselves and our self-protection. God wants to cover our sin AND protect us in our vulnerability, but these fig leaves are not his chosen instrument. He is wise enough to know that covering our sin, healing our hurt, and protecting us from sin's consequences will take much more than this breezy underwear we've woven. So notice (leaping ahead in the story) what God does in Genesis 3:21. He makes effective clothing for Adam and Eve. What is required for them to be clothed in "garments of skins"? The shedding of blood. Something had to die to cover their sin. This animal that gave its life to clothe and protect Adam and Eve becomes a precursor, a foreshadowing, of Jesus who gave his life, shed his blood, so that our sin might be covered and we might be healed in the refuge of his love.