As to
why the answer is both simple and complex.
The simple answer as to why 4e doesn't feel like D&D to many individuals is because too many sacred cows were changed in D&D
for them. I'm sure there will be many people who will respond here and say, "The sacred cows are all still there!" Well, they're not. That's okay, but you can't say that all of the same sacred cows of D&D are there.
Some of the sacred cows I'm talking about are things like, but not limited to:
- Rolling for hitpoints.
- Different to-hit modifiers for different classes.
- Radically different hitpoints between the classes.
- Saving throws, not defenses.
- Vancian magic. Yes, Vancian magic.
- Not everything ability being a combat option. For example, disguise self or the Ranger's animal empathy.
The list above are just examples. I'm sure I'm missing plenty and there will be people who argue that X is not a sacred cow. Nonetheless, they do indeed exist.
Now the reason that this gets complicated is because
the breaking point for everyone is different. Changing saving throws to Defenses might have
some people crying, "No! You've changed too much!" and it might have others shrugging and saying, "Eh. No big deal." or "I like it!"
For those people who are 4e fans, the breaking point was never reached. Or there was never any breaking point at all, so long as the game was still about kicking in the door, killing monsters, and taking their stuff.
So, it's perfectly understandable for there to be a complete disconnect between the various players of the game. Some will say too much has changed, others are okay with it. But what people are responding to when they say, "it doesn't feel like D&D to me" are those sacred cows that I was talking about.