Step 1: Concept Dephosphorization is the removal of phosphorus from molten metal into the slag phase.
Step 2: Meaning Phosphorus must first be oxidized to $P_{2}O_{5}$ and then stabilized in the slag.
Step 3: Analysis High oxygen potential (oxidizing conditions) is required for $P \rightarrow P_{2}O_{5}$. Since $P_{2}O_{5}$ is an acidic oxide, a basic slag (high CaO) is required to neutralize and hold it permanently in the slag.
Step 4: Conclusion Therefore, the necessary conditions are an oxidizing atmosphere and a basic slag.
Final Answer: (B)