To add on to the excellent explanation above, recombination can occur with only "paternal" genetic material. Remember, your father also has diploid germ cells before meiosis. So when the chromosomes line up during metaphase I, you have homologous pairs lined up side by side. These homologous pairs are derived from your paternal grandparents. In other words, your father's mother gave him one of those chromosomes and your father's father gave him the other. So when crossing over occurs, the gene(s) are crossing over between this homologous pair. Then anaphase occurs and you get haploid cells.