Honestly for me, I never liked using an engine to make games. Because I want to learn what is happening behind the scene. I want to learn the ins and outs of graphics programming. Using an engine to make a game does not really help me learn the depth of graphics programming that much. That is why I prefer diving into DirectX or OpenGL right away. However I feel like diving into OpenGL or DirectX right away has a very very steep learning curve, especially if you have never programmed a game before. That is why when I first tried to make a game, I used a friendly easy library like SFML, XNA, MonoGame, SDL, Allegro etc... After I learned the basics of those libraries I dove right into DirectX which made learning the API much easier.
of course if you don't care about programming much and you just want to make a game or become a game designer then using an existing engine is not a bad idea at all. It's actually better to use an engine because the time it would take you to code everything from scratch is a lot harder and longer.