There's no natural law that states assets or possessions can or should be maintained, to the benefit of others, after one's death. It's artificial. Not saying folks would or should reject the offer of inheritance, but to assume that there is some form of right, is wrong...
On one hand, not allowing one to pass-on assets to one's children, can be detrimental to us as a society because it removes much of the motivation of individuals to work hard and achieve wealth - in essence the message is: work only as much as you need in order to have a comfortable life, anything beyond that is pointless and a waste of your time because it will be taken off you anyway. So this can lead to economic stagnation.
The above is also another reason of why Communism does not work - the removal of the right to private property undermines people's motivation to work any more than the minimum required of them by the state. The removal of inheritance rights risks doing the same in free societies.
But - on the other hand, inheritance is unfair because it can be seen as a punitive measure against the children, 'punishing' or 'rewarding' them for the failings or success of their parents.
The modern thinking in Western societies is that children should not suffer as result of their parents' mistakes. Single mothers receive benefits not as reward for their effort of raising a family single-handed, but because not providing the mothers with financial assistance could mean that the children will have to go without.
Equally, universities are asked to make special accommodations for people from poorer backgrounds, based on the assumption that wealthier parents were able to invest more in the their children's education, and that the child's future should not be jeopardised by his or her parents' circumstances.
This is in stark contrast to Victorian times, where wives and children often moved to live in prison with the father simply because they had nowhere else to stay once the breadwinner was imprisoned. It was just 150 or so years ago when it still seemed to us reasonable that any failing of the father should rightly affect his entire family.
But this is the essence of a free economy... people with money can buy nice houses, live in good neighbourhoods, and then pass-on their assets to their children. The idea is that these rewards will motivate people to work harder and better themselves.
But this is again perceived as unfair on the children whose parents did not do as well, through no fault of the children.