Because it’s clever.
Cyprus is a small country in a good location. A country this small can not be self-sufficient and needs to trade with the world to earn its living. It needs to be competitive. Countries compete between themselves constantly – and not just in the Olympics.
Attracting foreign capital and business is a proven way to grow any national economy, to earn more and live better. In particular, the international financial services industry, in all its modern forms and shapes, creates jobs, career opportunities and income for a whole lot of people. It creates demand for professional services, commercial estate, communications and computer equipment, software and all sorts of business supplies. All that revenue filters down into all other sectors of the economy. It also generates tax revenue – at reasonable, not exorbitant, rates.
It’s just good management, really. Any country worth its name should do that.