A insect whose economic importance is both harmful and beneficial is the A. Tsetse fly B. Blackfly C. Butterfly

The insect whose economic importance is both harmful and beneficial is the butterfly.

• Harmful aspects: The larval stage (caterpillars) of some butterfly species can be agricultural pests, feeding on and damaging crops.
• Beneficial aspects: Butterflies are significant pollinators for many plants, including various crops, contributing to food production. They also play a role in the ecosystem as part of the food chain and are indicators of environmental health. Their aesthetic value supports ecotourism.

The other options are primarily harmful:

• Tsetse fly: Transmits trypanosomiasis (sleeping sickness) to humans and nagana to livestock, causing significant economic and health problems.
• Blackfly: Transmits onchocerciasis (river blindness) to humans and can be a biting nuisance to humans and livestock.

The final answer is $\boxed{\text{C}}$.