Olive oil has omega 3 fatty acid in it and most people are deficient on it. "Extra virgin" makes sure it's not oxidized or denatured due to heat and other processing.
The quality of other types of oil varies in terms of nutrition. If I feel adventurous, I am probably willing to try high quality coconut oil. But peanut oil predominantly has omega 6 fatty acid in it, I think. Hydrogenated oil is certainly a no-no for me. Extra virgin olive oil is not that expensive so I will probably stick to it for cleansing purposes.