"If two parties want to communicate with each other, why does it matters which side gets what percentage of the bill?"

Some Internet applications are unidirectional and can in principle (and sometimes in practice) can use datagram-oriented communication, without necessarily including information about the sender IP address; in other words from the ISP's perspective it may not be clear who the other party even is. The Internet is designed to support applications in general, including applications that have yet to be invented and which we may not be creative enough to even imagine. New protocols and applications are deployed with regularity.

All of that innovation and generality is dependent on net neutrality. Without net neutrality it is possible that deploying a new protocol would require coordination with one ISP after another. It is possible that an application that works at my house will fail to work at your house because your ISP refuses to provide service for that application. Maybe your ISP refuses to forward packets without a return address, or only supports two-party protocols (nobody said we cannot have a three-, four-, or N-party application -- except maybe some ISP).

"It makes sense for the health of the network for big companies like Netflix to have business relationships with the ISPs to push the servers closer to the edges"

That has nothing to do with net neutrality.

"The main argument for net neutrality is they are monopolies so we should beat them up"

No, the argument is that the utility of the Internet to society as a whole is maximized by neutrality and that the benefits far outweigh the cost of possibly lower ISP profits. It makes no difference if net neutrality is achieved by a regulation or by a competitive market, but for the vast majority of Americans there is no competitive market for ISPs. If you think a competitive ISP market is better than regulating a specific outcome, you need to have some proposal for setting up that market -- for example, re-instating the line-sharing requirements that gave rise to a competitive DSL market in the late 90s (a market which completely disappeared when those requirements were rescinded).

If you are not going to impose a line-sharing rule, then for the majority of Americans who have to deal with a local monopoly there will be abuses. Before net neutrality regulations, this was happening:

http://www.practicallynetworked.com/news/comcast.htm

Yes, that is Comcast blocking VPN protocols for residential customers, because if you want to work from home you have to buy their "professional" service, where VPNs are not blocked, because VPNs are only for professionals. I do not want to "beat up" Comcast just because they are a monopoly, but I do want to stop them from abusing their monopoly power by arbitrarily limiting the Internet applications their customers can use.

"legal power over the conduits of free speech and media."

Net neutrality promotes free speech on the Internet. Why should your ISP allow you to visit independent media websites? Why should an ISP allow anyone to exercise their free speech rights on The Daily Stormer? Net neutrality, of some form, is the reason you can consume whatever media you want to consume and freely engage in whatever form of speech you wish to engage in on the Internet without having to get your ISP's permission or to pay extra for the privilege (or maybe just having your ISP say, "sorry, we do not support Hacker News; have you tried Reddit or Slashdot?"). Maybe you are lucky enough to have a competitive ISP market in your area and you would just find another ISP, but, again, most Americans have either no choice or a very limited choice (e.g. one can either have Cable or DSL, which are not comparable, and a duopoly is not even remotely a competitive market).

Even without the Title II rules, the FCC still has the very legal power you object to; it is simply choosing not to exercise that power. The law as it is currently written allows the FCC to change the classification of ISPs back to Title II by following the same process used by Pai to reclassify ISPs under Title I. The courts found that the FCC had acted appropriately and within their power when ISPs were reclassified as Title II services. If you think that power is not something the FCC has then the burden is on you to change the law (good luck).