People outside The Faith will often look at passages like Romans 3 saying "All have Sinned" and that we are all Sinners as being a very misanthropic sentiment, and some Christians do also treat it that way including myself in the past when I was a more cynical person then I am now. However the problem is that the harshness of what "Sin" has come to mean to English speakers is no longer a good translation of the Greek or Hebrew concepts being referenced.
The Greek word that Paul and others are using in The New Testament is Hamartia and other forms of that word. Hamartia is in origin it seems an Archery term, most literally meaning "to miss the mark". Saying we are all Sinners is just Paul's way of saying nobody's perfect. Hence "come short of the glory of God". Now in just these early chapters of Romans it sounds like the consequences of merely being imperfect are pretty harsh, but this is in the context of him arguing agaisnt people way more judgmental then he is as he ultimately argues God has no intention of casting off even the worst of us.
When you look into literary analysis people talk about the concept of a "tragic flaw" that goes back to Aristotle's writings on the subject. That two word phrase is a translation of one word Aristotle used, Hamartia, I use Hamartia in this literary sense on another blog in my recent School Days analysis, but I wrote that already planning to write this and will probably go back and add links to this post. It amuses me how rarely this connection is made.
Red of OverlySarcasticProductions in her video on Tragedies says that a character's "Tragic Flaw" can also be the same as their virtue in a different context. And indeed I'd argue many of the best Superman stories involve the villain trying make a weakness of the very thing that makes him a Hero, and the same thing sometimes happens in Magical Girl Anime. Now many Christians may have trouble with the idea of this being applicable to The Bible's use of Hamartia, but remember when Paul called himself the Chief of Sinners in 1 Timothy 1:15? Well the Sin he means is confirmed by what he said earlier in the chapter to be his former status as a persecutor of the Church, and I would argue the very character traits that made Paul a dangerous enemy of The Gospel are what later made him a powerful advocate for it.
However I also think to a large extent the Jewish writers of The New Testament are using Hamartia to translate the Hebrew Bible's concept of Chet'/Chatta'/Chatta'ah, which is also frequently translated Sin and is the word used to name the Sin Offering of the Levitical Sacrificial system. When 2 Corinthians 5:21 says Jesus was made Sin for us, it's defining Him as a Sin Offering as the Hebrew of those Torah passages usually don't feature a word for offering as a separate word.
The Sin offering is defined as being offered to atone for violations of the Torah committed in Ignorance, the Trespass offering is for violations that were "high handed" (I've seen that suggested as the best translation), but neither is sufficient for actual capital offenses.
Hebrew Roots people will take 1 John 3:4's statement that "Sin is transgression of the Law" to prove that "yes The Torah does still apply no matter how often Paul appears to say otherwise". However that ignores how in The Torah not all transgressions of The Law are what the word "Sin" refers to.
On The Cross Jesus said "Father forgive them for they know not what they do", he defined their actions as Sins committed in ignorance even though by any normal standard they clearly aren't. Matthew 9:10-13 tells us to think of Sin as an illness that needs treatment, not a crime that needs punishment. Which is why many theologians see that statement from The Cross as ultimately applying to all the wrongdoings of all Mankind.
Related to this is the issue of cleanness and uncleanness in the Torah. People keep assuming those passages are about some mystical spiritual uncleanness, but they aren't, they are just literal hygiene laws.
Like how some people keep citing the verse saying Women are "unclean" when they menstruate as some proof of The Bible's horrible sexism. The Torah is imperfect (Hebrew 7) so I'm not going to claim there is nothing patriarchal about it. But that exact same chapter of Leviticus says the same about Male Ejaculate and the bodily waste everyone produces regardless of gender. It's just a passage telling us to wash our hands and shower.
"What about the incident where Jesus refused to wash his hands and then clearly moral uncleanness". The thing about that incident is that I'm wiling to bet Jesus had washed His hands, just not in the specific public ritual customary to that group of Pharisees. What He said there was in response to that they were thinking of spiritual cleanness because Hellenistic ideas were already infecting 1st Century Judaism.
