“In my opinion the point of high GDP is to provide better life for people. That’s higher GDP should lead to Higher HDI, otherwise it is not real development. What is your view?”
It does not strictly follow that higher GDP leads to higher HDI (Human Development Index).
GDP is a measure of what an economy produces. Consider an economy whose growth comes entirely from digging up raw materials then exporting them. The owners of the firms that export the commodities will make a killing, and they may hire a few extra workers in the process, but the rest of the population is essentially left out. Higher GDP in such a commodity-exporting economy is driven either by higher commodity prices (higher nominal growth) and/or higher commodity production or extraction (real growth), but the benefits to the population as a whole are nil unless something is done with that higher income.
You might now be wondering – well, that higher income is needed to even have a shot at improving HDI! It is true that higher income means more resources (including national resources through taxation) to invest and improve standards of living, but those investments need to actually improve standard of living, which is by no means a guarantee.
This indirectly brings us to the institutional setup of the country (or region or state). Improvements in standards of living and human development can come from a variety of changes that need not necessarily depend on higher income. They can come from a reallocation of existing resources towards areas that may better support development. They may come from greater personal freedoms, for example (and one need not believe in liberal democracy for that to be the case!). They may also come from more effective regulations that, for example, prevent the pollution of a local drinking supply, in turn helping to improve health outcomes via safe drinking water.
So, it does not strictly follow that higher GDP leads to HDI, and it does not have to be the case that any improvement in HDI depends on GDP growth. Though, it is true that higher incomes expand the capacity for greater investment and it is also true that higher incomes can be achieved from stronger institutions and effective, transparent, and credible laws.