Here is what I would say to that (while I agree with the basic premise of what is stated above).
Mat 1:21, And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins.
Tit 2:11, For the grace of God that bringeth salvation hath appeared to all men,
Tit 2:12, Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world;
Tit 2:13, Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ;
Tit 2:14, Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.
Tit 2:15, These things speak, and exhort, and rebuke with all authority. Let no man despise thee.
Yes indeed, if we are determined by the law to be sinners (Galatians 3:24, Romans 3:20, Psalms 19:7), it does indeed show us that we need Christ.
Christ is able to save us from our sins and to redeem us from all iniquity.
He gave us the Holy Spirit.
And through the Holy Spirit, if we walk not after the flesh but after the Spirit, the righteousness of the law will be fulfilled in us (Romans 8:4).
I would encourage my opponents as concerning doctrine to memorize that verse (Romans 8:4).
If they do, I think that they will integrate what it says into their thinking and will not have an argument with me any longer.