They have arguments that support their decision, but make no mistake - the only reason they care is because of Revenue.
If apps can be side-loaded, then they can circumvent AppStore fees, including In-App Purchase fees, which account for roughly 20% of their revenue. However, that 20% of revenue has a high profit margin since its digital goods and not physical hardware. I would wager that it's the biggest cash cow Apple has today. They will do anything to keep that system closed. It has 0% to do with security. The only way this will happen is court order, but that would be an overstep for the courts.
If this wasn't about money, they would easily allow side-loading how its done on Mac OS today, and how Android does it - by default on the approved store, with the option to allow side-loading in security settings.