He says that because the oxygen atoms are split between two different molecules in the products, the equation does not support the law of conservation of matter. Is your friend right? explain your answer?

According to conservation of matter, there should be equal amounts of all elements on both the reactant and product side.
Reactant:
1 Ca
1 C
1 O
Product:
1 Ca
1 C
3 O
Therefore, your friend is right because the law of conservation of matter is not followed in this chemical equation.