For God has imprisoned everyone in disobedience so he could have mercy on everyone. NLT
Does this scripture mean that God made everyone disobedient just to have mercy on us?
I do not believe so. In fact, the NKJV version tells it a little differently and doing so it lines up with more scripture.
32 For God has committed them all to disobedience, that He might have mercy on all. -Romans 11:32 NKJV
God doesn't "make" us be disobedient but rather he brings to light our disobedience so we can repent.
4 My conscience is clear, but that does not make me innocent. It is the Lord who judges me. 5Therefore judge nothing before the appointed time; wait until the Lord comes. He will bring to light what is hidden in darkness and will expose the motives of the heart. At that time each will receive their praise from God. -1 Corinthians 4:4-5
There is nothing concealed that will not be disclosed, or hidden that will not be made known. 3What you have said in the dark will be heard in the daylight, and what you have whispered in the ear in the inner rooms will be proclaimed from the roofs. "4'I tell you, my friends, do not be afraid of those who kill the body and after that can do no more. 5But I will show you whom you should fear: Fear him who, after your body has been killed, has authority to throw you into hell. Yes, I tell you, fear him. 6Are not five sparrows sold for two pennies? Yet not one of them is forgotten by God. 7Indeed, the very hairs of your head are all numbered. Don’t be afraid; you are worth more than many sparrows.'"- Luke 12:2-7
The point it is making is that according to God we are all disobedient and therefore we all need mercy and grace. He provided that grace through the finished work of Jesus on the cross.
Romans 12:33 (after the one you've just asked about:
33 Oh, the depth of the riches and wisdom and knowledge of God! How unfathomable (inscrutable, unsearchable) are His judgments (His decisions)! And how untraceable (mysterious, undiscoverable) are His ways (His methods, His paths)!
So even Paul marvelled at the statement you are asking about, because its quite a paradox when you first consider it.
By way of comparison, to Romans 11:32
7 And to keep me from being puffed up and too much elated by the exceeding greatness (preeminence) of these revelations, there was given me a thorn ([a]a splinter) in the flesh, a messenger of Satan, to rack and buffet and harass me, to keep me from being excessively exalted.
8 Three times I called upon the Lord and besought [Him] about this and begged that it might depart from me;
9 But He said to me, My grace (My favor and loving-kindness and mercy) is enough for you [sufficient against any danger and enables you to bear the trouble manfully]; for My strength and power are made perfect (fulfilled and completed) and [b]show themselves most effective in [your] weakness. Therefore, I will all the more gladly glory in my weaknesses and infirmities, that the strength and power of Christ (the Messiah) may rest (yes, may [c]pitch a tent over and dwell) upon me!
10 So for the sake of Christ, I am well pleased and take pleasure in infirmities, insults, hardships, persecutions, perplexities and distresses; for when I am weak [[d]in human strength], then am I [truly] strong (able, powerful [e]in divine strength).
The inspired writings say many things which seem counter-intuitive to what we learn, such as Isaiah 6:10 where it seems to imply stupidity is pushed upon people by God's will, but there is more to it than that. Compare: John 9:41
Ideally our less-than-perfect (sinful) circumstances should be humbling, the constant reminder of sin and it's results, which has the most important effect of showing the necessity of drawing closer to the means of our saving, God himself.
Note: The other side of these things is that a case is progressively built against the Devil who is the original and constant cause of man's falling. Revelation 12:10
Does the scripture mean God made us disobedient just to have mercy on us? No. God does not make us disobedient. Man, with the help of the enemy, chooses to be disobedient
Romans Chapter 11 is about the struggles of the Jews and the Gentiles in accepting the gospel. There was a remnant of the Jews that accepted the gospel, Romans 11;7.
And if some of the branches be broken off, and thou being a wild olive tree, wert grafted in among them, and with them partaketh of the root and fatness of the olive tree;
The olive tree is Israel, the wild olive tree is the Gentiles.
20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded but fear; 21 For if God spared not the natural branches, take heed lest he also spare not thee.
Romans 11;32 For God hath concluded them all in unbelief, that he might have mercy upon all.
No one in un belief is excluded, all, by the mercy of God may obtain salvation.