Calvinism is demonstrated, not through scripture, but through declarative statements with the twisting of Scripture, taking it out of context, and redefining of key words. You just demonstrated that in this post. We both agree in depravity but Total Inability is error. That is why you cannot reconcile this chapter or do a proper exposition of the chapter.
Let's consider the overall context and see what the Lord is saying.
In chapter one Paul addresses the wickedness of the Gentile world in general. He points out their idolatry and the consequences and all the evil that results from it.
However, in chapter two he begins with what one may call an imaginary conversation with a Jew. For example:
Rom 2:1 Therefore thou art inexcusable, O man, whosoever thou art that judgest: for wherein thou judgest another, thou condemnest thyself; for thou that judgest doest the same things.
and:
Rom 2:3 And thinkest thou this, O man, that judgest them which do such things, and doest the same, that thou shalt escape the judgment of God?
Paul continues this conversational style of writing into chapter three. In chapter two he condemns the sinfulness of the Jews, and then in chapter three he addresses both Jews and Gentiles together, thus 3:23,
"For ALL have sinned and come short of the glory of God."
But as you can see at the beginning of the chapter:
Rom 3:1 What advantage then hath the Jew? or what profit is there of circumcision?
Rom 3:2 Much every way: chiefly, because that unto them were committed the oracles of God.
--the conversation is continued.
We come to verse 9 and he asks this question to his imaginary Jew:
Rom 3:9
What then? are we better than they? No, in no wise: for we have before proved both Jews and Gentiles, that they are all under sin;
--There is the question. What is the answer?
Not only is the answer given in the second half of this verse, but he continues it in the next few verses.
Rom 3:10 As it is written, There is none righteous, no, not one:
Rom 3:11 There is none that understandeth, there is none that seeketh after God.
Rom 3:12 They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.
--This is a description of mankind. Man's heart is evil. It is deceitful above all things and desperately wicked. This is a general description of mankind.
It gets even more descriptive as he begins to quote from the book of Isaiah:
Rom 3:13 Their throat is an open sepulchre; with their tongues they have used deceit; the poison of asps is under their lips:
Rom 3:14 Whose mouth is full of cursing and bitterness:
Rom 3:15 Their feet are swift to shed blood:
Rom 3:16 Destruction and misery are in their ways:
Rom 3:17 And the way of peace have they not known:
Rom 3:18 There is no fear of God before their eyes.
Look around you, especially at the unsaved world:
Their throat is an open sepulchre (a metaphor--sepulchers stink).
With their tongues they have used deceit--Romans 3:4: all men are liars.
The poison of asps is under the lips--the cruelty of words, and what comes from the mouth.
--This is general statement of mankind. It is what we observe in general, but not what we can say about every single person.
Likewise as we go down each statement. About 1,000 were killed in Yemen by two suicide bombers. Wars are frequent. Men are violent. Men are swift to shed blood. It is common of mankind--but not common to every single man.
However, one by one man is convinced by this description that everyone is guilty of sin. We all have broken the law in some way or another. That is the point. We are guilty before God as law-breakers. Every person is.
Therefore:
Rom 3:19 Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God.
Under the law
all the world is guilty before God.
I hope you really understand the import of this statement.
The world here does not refer to just the elect
as so many Calvinists adamantly affirm that it does in John 3:16. There is no reason in either verse for "the world" to be confined to "the elect." In fact it never does. Only Calvinism necessitates such an interpretation. The world means everyone, just as it says, in both verses.
All the world is found to be guilty before God: ALL, excluding no one.
Therefore:
Rom 3:20 Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.
--It is not by the law; not by works that one is saved. The law simply points out our sin.
Rom 3:21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
Rom 3:22 Even
the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
--How does righteousness come? How is it attainable?
It is not by the law. It is not by works.
It is by faith in Christ! This is the great and wondrous message of the Bible. Salvation is by faith. Not once here is the doctrine of "unconditional election" mentioned, nor "limited atonement," nor "irresistible grace," but salvation in Christ by faith.
Rom 3:24 Being justified freely by his grace through the redemption that is in Christ Jesus:
--How is one justified?
Freely by his grace. It is through the redemption that we have in Christ.
Rom 3:25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;
--What has happened here?
God made Christ to be a propitiation for our sins. We accept that by faith. The sacrifice that was made was made once and for all, for all the world. It is made efficacious through faith in his blood, in his sacrifice. That is how we obtain forgiveness of sins--through faith.
Paul makes some concluding remarks such as:
Rom 3:28 Therefore we conclude that a man is justified by faith without the deeds of the law.
--Notice he still using this conversational style.
But it is faith that justifies a person, not Calvinism.