How do you answer Calvinists who say that rejecting monergism means taking partial credit for your own salvation?

God gets all the credit for everything. As Augustine said, quoting 1 Corinthians 4:7, everything you have is a gift from God, so you cannot take credit for anything. That is the foundation. Ephesians 2:8-9 says it is by grace you have been saved through faith, and this is not from yourselves, it is the gift of God, not by works, so that no one can boast. In the Greek, the word 'it' is neuter, so it cannot refer specifically to faith, works, or grace, which are all feminine; 'it' refers to the whole process. Even your ability to accept God is a gift from God. So we Catholics do not pretend that part of salvation is our own doing. Now here is the question: God has given us the gift, and will we use it or abuse it? That is where free will comes in. When we say man has a free will, we are not saying he engineered any of this; he is just a cog in the wheel and created nothing of the process. But God decided to give him an uncoerced, unmitigated free will. So God gives the gift of faith and grace, and we can either use it or abuse it. That is not works-salvation; it is simply using the gift God gave. When Protestants point to John 6:37, 'all that the Father gives me will come to me,' they read it only one way, as if the Father picks them without their free will, but the verse does not say how they got there. They could have used their free will to accept God's grace, after which God gathered them and gave them to Christ. Much of this comes from reading Calvin's theology into the text.