I believe that the atonement of Jesus Christ on the cross was designed not to make salvation possible for all people (that is, to pay for the sins of every person), but to infallibly secure the salvation of a chosen people for God (that is, to pay for the sins of the elect and purchase every part of their salvation). One of most difficult texts for this view is 2 Peter 2:1, which says, "But false prophets also rose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction." This text may seem at first glance that Christ also paid for the sins of false teachers going to Hell, thus entirely disproving limited atonement. However, this is not what the verse is actually saying. That is really reading a lot into the text that is simply not there. Here are the notes from the ESV MacArthur Study Bible.
"denying the Master. The phrase exposes the depth of the crime and guilt of the false teachers. This unusual Greek word for 'Master' or 'Lord' appears 10 times in the NT and means one who has supreme authority, whether human authority or divine authority. Peter warns here that false prophets deny the sovereign lordship of Jesus Christ. Though their heresies may include the denial of the virgin birth, deity, bodily resurrection, and second coming of Christ, the false teachers' basic error is that they will not submit their lives to the rule of Christ. All false religions have an erroneous Christology. who bought them. The terms that Peter used here are more analogical than theological, speaking of a human master over a household. The master bought slaves, and the slaves owed the master allegiance as their sovereign. (For an OT parallel, see Deut. 32:5-6, where God is said to have bought Israel, though they rejected him.) Doctrinally, this analogy can be viewed as responsibility for submission to God, which the false teachers had refused. Beyond this, they are probably claiming that they were Christians, so that the Lord had actually bought them personally. With some sarcasm, Peter mocks such a claim by writing of their coming damnation. Thus, the passage is describing the sinister character of the false teachers who claim Christ, but deny his lordship over their lives."
"denying the Master. The phrase exposes the depth of the crime and guilt of the false teachers. This unusual Greek word for 'Master' or 'Lord' appears 10 times in the NT and means one who has supreme authority, whether human authority or divine authority. Peter warns here that false prophets deny the sovereign lordship of Jesus Christ. Though their heresies may include the denial of the virgin birth, deity, bodily resurrection, and second coming of Christ, the false teachers' basic error is that they will not submit their lives to the rule of Christ. All false religions have an erroneous Christology. who bought them. The terms that Peter used here are more analogical than theological, speaking of a human master over a household. The master bought slaves, and the slaves owed the master allegiance as their sovereign. (For an OT parallel, see Deut. 32:5-6, where God is said to have bought Israel, though they rejected him.) Doctrinally, this analogy can be viewed as responsibility for submission to God, which the false teachers had refused. Beyond this, they are probably claiming that they were Christians, so that the Lord had actually bought them personally. With some sarcasm, Peter mocks such a claim by writing of their coming damnation. Thus, the passage is describing the sinister character of the false teachers who claim Christ, but deny his lordship over their lives."