They also want the ability to charge content providers (such as Netflix) for your ability to access their content.
It seems carriers want to charge twice for the same bandwidth
No. They only charge Netflix to host Netflix on Verizon's network. That's what the agreements were really all about. Netflix was having problems with Cogent and they either chose to ignore this fact and blame ISPs, or they were too stupid to realize that Cogent was actually throttling them during peak hours.
Verizon and Comcast were blamed, when the fault really lay with Netflix and Cogent.
What's really hilarious about this? If net neutrality passes the ISPs lose control over their own networks. When they become flooded by ever-increasing HD video streaming, it means they can't throttle Netflix et al and so other higher-priority traffic suffers. Real-time gaming packets? Oh treat them the same as email or Netflix packets. Yet many ignorant Americans think Net Neutrality is some kind wonderful panacea to a problem that never really existed in the first place!