Meiosis copies the DNA once, then divides twice, so one diploid cell becomes four haploid gametes. On the way it shuffles the alleles: partner chromosomes swap pieces, and the pairs line up by chance. Step through the phases and count the different gametes: up to four with crossing over on, only two kinds without it. Flipping the line-up changes which alleles travel together, not how many kinds one cell makes, so independent assortment adds variety across many cells, not within one.
Meiosis makes four haploid gametes. Crossing over in prophase I can make all four from one cell different; independent assortment in metaphase I lines pairs up differently in different cells, adding variety across many cells.