If you plan on playing Minecraft moving forward, you're going to need a Microsoft account. Mojang has made the announcement on the official Minecraft website, and explained the move with the following reasoning.
Change can also pave the way for a better future. That’s why we’ve decided that moving forward, all of our games will require a Microsoft account to play. Why? Think of it as moving house; when you outgrow one place, you move on to the next. It involves a logistic effort, but once you’re settled in your new home, you realize you’d do it ten times over just for that extra room. Except in our case, the extra room is all of these features, from which all Microsoft accounts will benefit:
Increased security for your account with two-factor authentication. In other words, it’s harder for someone to access your account without your permission.
All your PC Minecraft games will be connected to the same account. Currently, that’s Minecraft and Minecraft Dungeons, but who knows what we'll do next?
Improved parental controls to help keep kids safe when playing online.
Chat and invitation blocking.
Now just to be clear, migrating from Mojang to Microsoft accounts is mandatory. If you don’t make the move, in several months you won’t be able to log in anymore – which means you won’t be able to play either.
There's really no way around this move, so you might as well make the change now while you can. Full details on how to create an account can be found here.