Hi, ckim. This is a great question, and one deserving of much thought.
I've found it helpful to think about it in this way. If your parents were Israelites during the time of Egyptian slavery, what would you be when you were born? You would be a slave of course. You could argue to the Egyptians about how unfair it is that you are their slave just because your parents are slaves, but I don't think they would listen to you.
In the same way, when Adam and Eve sinned, they became slaves to sin (Romans 6:6). Parents who are slaves to sin have children who are born slaves to sin. As such, these children are predisposed to sin as soon as they are born -- even before, as David says in Psalm 51:5, "Behold, I was brought forth in iniquity, and in sin did my mother conceive me." It is not only that all people will choose to sin, but they are even corrupted in their hearts from their conception. This is a very hard idea to swallow, especially because little children seem so innocent in our eyes (and compared to most adults, it is easy to see why).
But if it is with great pain that we accept being born into sin through Adam, justly deserving God's wrath, it is with great joy that we accept being born again into righteousness through Christ, justly deserving God's love and perfect acceptance of us! I would even say that it is impossible to truly believe in how sinful we are, even at birth, without first seeing that God has already redeemed us. In Isaiah 44:22 God tells His people, "I have blotted out your transgressions like a cloud and your sins like mist; return to me, for I have redeemed you." Notice that God does not say, "Return to me, and then I'll redeem you," but He says the opposite: "Return to me, for I have redeemed you." How beautiful is God's love for us!
Here's another way to think about this that might help. Let's say you're a parent, and you have children. Chances are that you love your children, and you want to give them all the benefits you can as a parent. You want to give them a home, food, clothing, education, and, most importantly, your love. And it is perfectly right for you to give them these things, because they are yours to give. It follows that we would think it very unfair for someone to tell you that you are not allowed to give your children these things because your children have done nothing of themselves to earn them. When it comes to original sin, then, it is not logical for us to say that children deserve to have what their parents can give them while limiting it only to good things.
My last example, and probably the most shocking, is this. People have often found just reasons to end certain people's lives. Take a mass murderer for example. We kill this individual because we say he/she deserves it. Throughout the whole Bible God has chosen to kill many people. What we often forget is that in ending one person's life, we also end any chance of their having children. In essence, because the father/mother deserves to die, we say that the children do not deserve to be born. This is not an argument against killing -- how can I call what God has done a sin? No, it is an argument for the fairness of original sin.
I hope this helped a little bit. Always keep in mind the greatness of God's love for us when thinking about the wretchedness of our sin. I love this quote by Luther: "For every one look you take at your sin, take ten looks at the cross."
Grace and peace in Christ Jesus.