'Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith. Therefore we conclude that a man is justified by faith without the deeds of the law. ' Romans 3: 27-28

I'll spell it out. Boasting is futile because works don't make you righteous. There is only one source of righteousness. There is only one person who is righteous. He endows you with His righteousness. You can't give it to yourself.  You have to go to the righteousness store.  He is at the counter and you purchase it from Him.

'Because thou sayest, I am rich, and increased with goods, and have need of nothing; and knowest not that thou art wretched, and miserable, and poor, and blind, and naked: I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed, and that the shame of thy nakedness do not appear; and anoint thine eyes with eyesalve, that thou mayest see.' Revelations 3: 17-18

Your own righteousness is like going to the dump or refuse pile. vs his righteousness store.  How do you buy it? What exchange do you make for it? What is the means? It's not money. It is faith. Your faith in the righteous works of God.  So boasting isn't going to help you. The basis of your boast is irrelevant.

Paul must have just been reading from Jeremiah when he wrote these verses. Jeremiah lamenting over Zion said, 'Thus saith the LORD, Let not the wise man glory in his wisdom, neither let the mighty man glory in his might, let not the rich man glory in his riches: But let him that glorieth glory in this, that he understandeth and knoweth me, that I am the LORD which exercise lovingkindness, judgment, and righteousness, in the earth: for in these things I delight, saith the LORD.' Jeremiah 9: 23

The conclusion of these first three chapters is that a man is justified by faith without the deeds of the law and that 'therefore being justified by faith, we have peace with God through our Lord Jesus Christ.' Romans 5:1  

What does that mean? It means we are 'justified by the blood of Jesus Christ. 'Much more then, being now justified by his blood, we shall be saved from wrath through him.' Romans 5:  9