Each egg or sperm contains half of each pair of chromosomes from a mother and a father respectively. The human DNA set has 23 pairs of chromosomes. If you imagine putting each pair in a separate bag and then pulling one from each bag to make up an egg or sperm you can understand that there are multiple combinations of chromosomes that could end up in each egg or sperm which is why they are not identical. Given that for every egg that may be fertilised there are multiple sperm there are again multiple different combinations of genes which may be combined when an embryo is formed. This is why siblings only have the same genes when they are identical twins and have formed due to the splitting of one embryo in two.