You gotta have an aptitude for boxing. In boxing things are learned in pieces, and like you said a fighter has to put two and two together and figure things out on their own. When Ray Leonard walked into a boxing club he didn't even know how to hold his hands up right, when they asked him to he looked like a John L. Sullivan. Except Leonard had enthusiasm, you can call it drive, commitment or whatever you want but enthusiasm goes a long way. Leonard as with many good fighters made sense of the moves and learned the moves as fast and as fast as they were taught them.

The fighters who fail horribly can't make any sense of things. As for "feel" a fighter needs an intuition that acts accordingly to the fight without the fight talking to himself in his head. Training shouldn't be canned dress rehearsal; it should be to get condition and to build an aptitude, a 'feel' for the fight and the guy in front of them. A lot of guys miss the point and start asking how to get a 6 pack, how to get the right muscle fibres, or get caught up on one point while the real fighters keep getting better. If you want the works you gotta learn the rope through sparring/fighting smart, not by pushing iron or looking for a magic bullet that's going to make things easy.

Having a feel for what's going on isn’t talking to yourself in your head, it’s more of a sense than it is thinking about it. In a fight too much thinking and not acting fast enough will get people knocked out. It’s okay to build on thoughts while in training but while in the ring these have to be made instinctive. Instincts gotta made in the rigors of training particularly sparring and past fights.

Past the talking to yourself stage, here are some instincts a fighter feels:
-How to move around the ring, how to do the right moves defensively/offensively...
-Looking to see what punches the opponent commits to.
-Finding what makes the opponent commit to a punch.
-Drawing the opponent in; the setup.
-Seeing if the opponent makes any preliminary moves, what do they telegraph?
-See how they shift their weight before they punch, what do their arms and body say before and while they punch...
-How do they use their jab, clinch, etc... etc...

Now I could keep going but I'm just adding to the point Tom made about fighters who just get it and the failures who are far from it. If any of you fighters want to be a good fighter then you gotta figure things out on deeper level and put it all into action knowingly and instinctively. This is what separates the haves and the have-nots in the ring.