"Many" is a Biblical idiom that often means "all." Daniel 12:2 speaks of the general resurrection and states, "And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt." Here "many" means "all." On the last day everyone will be resurrected, not just some people. The Catechism of the Catholic Church points out that that when Romans 5:12 states that by Adam's disobedience "many" were made sinners, it means that all men were made sinners (CCC 402).
Christ did shed his blood for all men in some sense. 1 John 2:2 says, "[Jesus] is the expiation for our sins, and not for ours only but also for the sins of the whole world." It is by the shedding of Christ's blood that the sins of the world could be forgiven.
It is surprising that some Catholic traditionalists reject the statement that Christ's blood was shed for all, since ordinarily the rejection of this proposition may be regarded as the heresy of Jansenism. In 1658 Pope Innocent X condemned as heretical the Jansenist proposition that "it is Semi-Pelagian to say that Christ died or shed his blood for all men without exception." The pope declared that this was heretical if understood to mean that Christ died only for the predestined.