Because it's a smaller upfront cost, and a "pay per usage" cost ongoing. Many people don't want to (for example) dedicate the space to a large dvd collection for something they're only going to watch once, or to buy a media cupboard to hold two extra dvds. People don't want the hassle of reselling/searching the second hand market (where companies like eBay provide value, but friction and risk at the same time as anyone who has ever had an "item not received" case opened against them will tell you).
That's a common theory among people who hold a minority preference in a market, but it's almost invariably wrong. On aggregate, people tend to be rational. And there's plenty of valid and rational reasons for preferring to rent vs owning. Some reasons I can think of: lower cost, convenience (don't need to go to a store or wait for a shipment, doesn't take space in your apartment), not having to worry about hardware breaking, not having to worry about upgrading when a new model comes out, not having to worry about backups, portability, access to a huge catalog, personalized experience, ability to easily switch service providers, etc. It's not hard for me to understand why many people would prefer to rent.
If only that could be true. Economics would be more simple, and maybe actually a science.
Modern economics is nearly entirely how to deal with the fact that individual actors are indeed not rational according to the traditional definition of the term. Which is why advertising works so well.
It's a model that mostly reflects reality. I find the alternative much more unbelievable (e.g. that this trend is the result of general ignorance and dumbness). It's simply more likely that your personal preference simply isn't shared by the majority.