Few actually understand what net neutrality really is. It's not government regulation (as much as some would like to think), nor does it change anything that is already in place. It simply states that companies can't violate their contract with their customers to provide internet access at a certain speed, by ripping off both the content provider and the content consumer in limiting the speeds of certain types of access.
This is not at all close to the argument "the post office has to ship things at the same price regardless of size." For one, the internet is not comparable to the post office, because, by technology standards, all packets are limited to 1500 bytes. Due to this technological limitation, it would be like the post office trying to charge different fees for a standard letter envelope and a standard letter envelope with a half an ounce packet of sugar.
Two, net neutrality does not force a one-price model for all speeds. As a model, it believes that ISPs should charge more for more speed. The difference is that net neutrality does not allow companies to say "your internet speed for your $50/month plan is 25 MBPS" while in a small print they write "except for access to Google, YouTube, Netflix, and Fox News." If companies are allowed to limit speed to certain sites by law, then by law and technological ability they are allowed to block access to legal websites, in order to charge more for their own competing services, which are often of poorer quality.
A better post office analogy would be this:
The post office provides different shipment plans, $10/month for 50 packages, $20/month for 100, and so on. Then, the post office all of a sudden decides to start tracking the addresses you're shipping to and sees that you're mailing 75 of your 100 shipments under your $20 plan to a certain address in Pennsylvania. They contact you and say, "from now on, if you wanna ship to that address, you'll have to purchase the $30/month plan for 200 packages or we won't ship to that address." This is exactly what net neutrality is trying to prevent.