Its simple. Let me break it down to you. Synthetic oil is not real mineral oil. It is built using various chemicals so it has longer life span than a conventional mineral oil and it has cleaning agents which keeps the engine clean by absorbing oil deposits in an engine,
If the car is driven on mineral oil from the start of its life, it tends to build up little bit of oil deposits/sludge in the engine. So a layer will be built up in the engine which might cover the worn areas of the engine and seals. So switching to synthetic after such age of the engine, it will eat away those deposits. If the deposits are heavy then it might result in leakage of seals, increased engine noise or also in some cases failure of the engine. In some cases switching to synthetic caused little or no issue but there have been comparatively more complaints by users after switching to synthetic on old cars.
So, to be on the safer side, It is best to use the oil previously used in the car. But still if you want to switch, you should first try semi-synthetic oil and after 2-3 intervals if engine remains fine, you can pour in synthetic and see how your engine responds.
But my recommendation will be mineral oil or semi-synthetic. Hope you get the point now.