Networks don't want Aereo as it will rock the boat and introduce competition in markets that have long been dominated by oligopolies. In most areas, you have one cable company that services the area, and if you're lucky, the local telco might also offer television service. You also have Dish and DirecTV.
Most networks opt to charge the cable/telco/satellite company a fee instead of forcing them to be carried as a must-carry station. If a more convenient or alternate source of locals were available, it could result in lower revenues from fees. So stations have a reason to want to keep availability scarce. Networks obviously have a vested interest in keeping the stations happy, so they fight the fight. Cable companies also join in as they may also own the local tv station. Or the TV network. Or are the content producers. Or all the above.
It's all about maximizing revenue while stifling competition that may take a portion of their pie.