This short quote by Charles Spurgeon really strikes at the heart of the objection to Particular Atonement. You have to think this through.
The Arminians say, 'Christ died for all men.' Ask them what they mean by it. Did Christ die so as to secure the salvation of all men? They say, 'No, certainly not.' We ask them the next question: Did Christ die so as to secure the salvation of any man in particular? They answer 'No.' They are obliged to admit this, if they are consistent. They say, 'No; Christ has died that any man may be saved if ?' and then follow certain conditions of salvation. Now, who is it that limits the death of Christ? Why, you. You say that Christ did not die so as infallibly to secure the salvation of anybody. We beg your pardon, when you say we limit Christ's death; we say, 'No, my dear sir, it is you that do it.' We say Christ so died that he infallibly secured the salvation of a multitude that no man can number, who through Christ's death not only may be saved, but are saved, must be saved and cannot by any possibility run the hazard of being anything but saved. You are welcome to your atonement; you may keep it. We will never renounce ours for the sake of it.