Why do daughter cells contain the same amount of DNA as original cell?

DNA makes a copy of itself, in a cell that is undergoing fission. It is an accurate copy (not necessarily 100% accurate, but very close). That is the basis of genetic inheritance. If the daughter cell did not contain the same DNA as the parent cell, it would not be the same species. Only in sexual gametes do we get an exception, in which case each of two parents contributes (approximately) half the DNA.