Microsoft is first to make online multiplayer on consoles a major feature.
Microsoft realizes they can charge for it since there's no competition.
Microsoft charges for it, and since no one else does the same thing for any cheaper, people accept it.
7th gen roles around. Sony and Nintendo attempt to combat it by making their services free.
People still are paying for Xbox Live because they're accustomed to it, and it was arguably more featured.
8th gen rolls around and Sony realizes that people would probably be willing to pay for it on Playstation if they gave gamers some incentives to do so, and slowly works up to doing so.
Nintendo realizes their online is not featured enough for people to pay for it, chooses not to.
Meanwhile, PC gamers can easily pirate games, and many games have free online. PC games had free online for long enough that if a company decided to start charging for it, people wouldn't pay for it, because there are other, free options.
TL;DR:
Online PC games have always had free competition, so aside from MMOs, paid online services are quickly rejected by consumers.
Online console games didn't really have free competition when they started up, so Microsoft was able to capitalize on that and make a shit ton of money. Then Sony realized they could probably do the same thing.