In the first case is often a case of wood thievery, a crime for profit. Can be also revenge (as in the sycamore gap) or just mental insanity.
In the second case can be a legal or illegal move. In some countries a centenary tree can't be chopped unless you ask for a special permit to the government. It the tree is a danger for historical or valuable structures, severe pruning or chopping can be allowed. If the tree has special historical, aesthetic or monumental value, the permit can be denied, even if the tree is in your property.
Your mileage may vary depending on the country.
That said, only an idiot would chop a centenary tree in their property if is not causing any serious problem to foundations or people. The presence of this tree will increase greatly the value of the property. Homes with trees have a much higher monetary value. Homes with ancient trees play in a special league of luxury.
It may even provide some special bonuses, like a decent fruit harvest each year, fertile soil, as touristic trap (see Beijin Ditan park Ginkgos, for example), or simply saving solid money on the energy bill of the house.
People buy property purely as an investment, it would seem that to some people it is a simple choice.
Perhaps they could replant with Leylandii?