I mentioned this in the L&L retrospective thread.I also don't think "train an animal to fight" is, or even should be, a purely magical effect. Real-world cultures did it all the time--the forebears of the modern Rottweiler (probably) included the preferred breed of war dog in ancient Rome. In a setting where things that are physically impossible in our world are achievable by purely "mundane" characters like Fighters, I fail to see why Rangers HAVE to be magical in order to have a well-trained war animal. Or, in other words, I don't think it's a supernatural bond, and I think several of the class-specific "spells" the 5e ranger gets should just be abilities. This is almost surely a matter of taste.
There are a number of abilities that D&D has, traditionally, categorised as magical rather than mundane because that was a way of rationing them: the ability to blind, maim etc; the ability to befriend or persuade people; the ability to have an animal companion; the ability to urge on one's companions (ie hp recovery); etc.
4e broke away from this in some respects. 5e has generally gone back to it.
I think this tradition is part of what makes it hard to model fictional archetypes and fictional stories using D&D.