Pinker on why there are 2 sexes:

Why do we make one big egg and lots of little sperm, instead of two equal blobs that coalesce like mercury? It is because the cell that is to become the baby cannot be just a bag of genes; it needs the metabolic machinery of the rest of a cell. Some of that machinery, the mitochondria, has its own genes, the famous mitochondrial DNA which is so useful in dating evolutionary splits. Like all genes, the ones in mitochondria are selected to replicate ruthlessly. And that is why a cell formed by fusing two equal cells faces trouble. The mitochondria of one parent and the mitochondria of the other parent wage a ferocious war for survival inside it. Mitochondria from each parent  will murder their counterparts from the other, leaving the fused cell dangerously underpowered. The genes for the rest of the cell (the ones in the nucleus) suffer from the crippling of the cell, so they evolve a way of heading off the internecine warfare. In each pair of parents, one “agrees” to a unilateral disarmament. It contributes a cell that provides no metabolic machinery, just naked DNA for the new nucleus. The species reproduces by fusing a big cell that contains a half-set of genes plus all the necessary machinery with a small cell that contains a half-set of genes and nothing else. […]

Once an organism has taken that first step, the specialization of its sex cells can only escalate. A sperm is small and cheap, so the organism might as well make many of them, and give them outboard motors to get to the egg quickly, and an organ to launch them on their way. The egg is big and precious, so the organism had better give it a head start by packing it with food and a protective cover. That makes it more expensive still, so to protect the investment the organism evolves organs that let the fertilized egg grow inside the body and absorb even more food, and that release the new offspring only when it is large enough to survive.