I know a priest who frequently says that Jesus Christ died on the cross in His humanity and not in His divinity. God does not die, he says.
I have heard from others that God the Son became Man and died as God and Man on the cross for our salvation.
Which of these is true?
Here is an excerpt from a traditional, conservative, pre-VCII manual of Catholic Dogma. Its virtue is its striving after detail and for precision and accuracy. Still, it is the author's opinion, a rule as he says.
Dr. Ludwig Ott
Fundamentals of Catholic DogmaTAN Books and Publishers, Inc. 1974; page 161:
2. Rules Concerning the Predication of Idioms
The nature of the Hypostatic Union is such that while on the one hand things pertaining to both the Divine and the human nature can be attributed to the person of Christ, on the other hand things specifically belonging to one nature cannot be predicated of the other nature. Since concrete terms (God, Son of God, Man, Son of Man, Christ the Almighty) designate the Hypostasis and abstract terms (Godhead, humanity, omnipotence) the nature, the following rule may be laid down : commuuicatio idiomatum fit in concreto, non in abstracto. The communication of idioms is valid for concrete terms not for abstract ones. So, for example: The Son of Man died on the Cross; Jesus created the world. The rule is not valid if there be reduplication, by reduplication the concrete term is limited to one nature. Thus it is false to say " Christ has suffered as God." " Christ created the world as a human being." It must also be observed that the essential parts of the human nature, body and soul are referred to the nature, whose parts they are. Thus it is false to say: "Christ's soul is omniscient," " Christ's body is ubiquitous."
Further, predication of idioms is valid in positive statements not in negative ones, as nothing may be denied to Christ which belongs to Him according to either nature. One, therefore, may not say : "The Son of God has not suffered," "Jesus is not almighty." Assertions liable to be misunderstood should be protected by clarifying additions like "as God," "as man," for example. "Christ, as man, is a creature."
Applying these rules I get:
Jesus Christ died on the cross.
Jesus Christ died on the cross in His humanity.
God the Son became Man and died as Man on the cross for our salvation.
God the Son died on the cross for our salvation.
God the Son, true God and true Man, died on the cross for our salvation.
Even in following the rules, however, Ott rightly recommends "Assertions liable to be misunderstood should be protected by clarifying additions."