For all have sinned and fall short of the glory of God (Romans 3:23)
Paul says in Romans that everybody has sinned and it's impossible to keep the commandments. Why bother trying?
There are three major problems with this.
First, there is usually a "for salvation" assumption implied in the objection— it is impossible to keep the commandments for salvation, so why bother trying?
The commandments were never intended to achieve salvation so the question itself is flawed. It's like asking the question, "It is impossible for my blender to fly me to London, so why bother using the blender?"
The answer is simple. Use the blender for its intended purpose. Like making a smoothie maybe. The Law should likewise be used for its intended purpose.
Second, the Bible says the exact opposite.
After delivering the commandments for the second time, God tells the Israelites that the commandments are not too difficult for them:
For this commandment which I command you today is not too difficult for you, nor is it out of reach. It is not in heaven, that you should say, 'Who will go up to heaven for us to get it for us and make us hear it, that we may observe it?' Nor is it beyond the sea, that you should say, 'Who will cross the sea for us to get it for us and make us hear it, that we may observe it?' But the word is very near you, in your mouth and in your heart, that you may observe it. (Deuteronomy 30:11-14)
Paul connects this declaration in Deuteronomy to the life of faith he proclaims in his letter to the Romans:
But the righteousness based on faith speaks as follows: "DO NOT SAY IN YOUR HEART, 'WHO WILL ASCEND INTO HEAVEN?' (that is, to bring Christ down), or 'WHO WILL DESCEND INTO THE ABYSS?' (that is, to bring Christ up from the dead)." But what does it say? "THE WORD IS NEAR YOU, IN YOUR MOUTH AND IN YOUR HEART"--that is, the word of faith which we are preaching, that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved; for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. For the Scripture says, "whoever believes in him will not be disappointed." (Romans 10:6-11)
The words in ALL CAPITALS is where Paul quotes the Deuteronomy passage from above.
So the "word of faith" that Paul is preaching is the same as the teaching of Moses in Deuteronomy!
After all, says Paul, "I can do all things through [Christ] who strengthens me." (Philippians 4:13)
Third, when saying it is impossible to "keep" the commandments, the person objecting usually means it is impossible to "perform" or "do" the commandments. Every place in the Law where we are commanded to "keep" the commandments, the Hebrew word שָׁמַר [shamar] is used. Shamar does not mean to "perform", it means to "guard" or "protect" the commandments. It is possible to guard and protect the commandments. By reading Scripture with our families, holding fast to the canon of Scripture (including the books of Moses), teaching the whole counsel of G-d, etc we are "guarding" and "protecting" the commandments... we are "keeping" the commandments.
Be sure to also check out Jay Carper's insightful response to the question "Is it possible to keep the Law?"