From the Roman Catholic Mass (spoken by the congregation as part of a call-and-response):
"Lord, I am unworthy to receive you, but only say the word and I shall be healed"
The idea that we are unworthy of god's forgiveness was drilled into me from a young age. It makes perfect sense if you don't think about it, the idea that a Supreme Being can create something, and then blame that something for not living up to It's standards. Like, if I burn a steak I don't curse the cow.
As others have mentioned, the idea of original sin was created to justify the necessity of Christ's sacrifice for everyone, no matter how virtuous, even a new born baby that hasn't had a chance to sin - we are all born evil. This has nothing to do with Jesus saying "we're all sinners." That was just an admonishment to keep our self-righteousness in check, as none of us are perfect. Original sin goes far beyond "nobody is perfect" into mind-fuck territory. "We're all sinners" means none of us are fit to condemn another; Original sin means we are all fit to be condemned.
Original sins says: You are unworthy of God's love, but if you abase yourself and grovel you will be saved by grace.
The priest at the church I grew up in gave a homily when I was around 10 or 12 where he talked about the above quoted part of the mass; he contested it, saying that if we weren't worthy of god's love and forgiveness it wouldn't be offered to us. He was genuinely bothered by this particular part of Catholic doctrine. A light in the darkness as it were.