If you want to know all the reasons I'm wrong about a sandbox campaign, you should first read this, and then you should read this. I include these links in the interest of providing fair and equal consideration to all sides of this debate.
You may have some trouble understanding what's written there. Except for the stream of statements that I'm wrong, I did.
Here's the thing about definitions. If something is not defined, it is very hard to argue about it. My sincerest desire where it comes to understanding something begins with having that thing defined, and in a manner absolutely clear to everyone involved. I am less concerned about who is, and who is not, hurt by the definition or by the labels that definition provides than I am that everyone understands what word means what thing.
The links above provide an alternate definition for a sandbox. It isn't very clearly defined. It seems to be very convenient for the author's self-aggrandizement. Extrapolated, it would seem to allow virtually any action to be interpreted in any manner that the author might wish. As a definition, it simply isn't one.
It is, however, a very emotional appeal towards a label dearly wished for, for reasons that should seem clear:
Sandboxes have more credibility than railroads.
The gentle reader will take note. This argument has been going on a long time, and in that time a definite connotation has been obtained for the two words themselves. Regardless of what they mean, everyone has more or less come to accept that a "sandbox" campaign is "good," while a "railroad" campaign is "bad."
This is in some ways an achievement.
It is not, however, indicative of a general desire to surrender the railroading of players. No, far from it. The connotation has only encouraged a desire to stop being identified as railroaders.
To this end, any amount of bullshit is acceptable. To this end, justifications and obfuscations, appeals to emotion, the need to repeatedly define one's world as alive or vibrant (actually the same thing, but still, nuance & nuance), etcetera.
I am fine with this. No one wants the railroad label. But please, dear gentle reader, take note. It remains the case that IF you attempt a definition, and if that definition clearly delineates a certain number of people as being part of the connotatively undesirable camp, there will always arise a minority who will suddenly, earnestly, argue that they are NOT of that camp, that they are bitter about being thrown into that camp, and that clearly the definition is wrong by virtue of this utter certainty that they have.
This will happen in every case, even if you make no mention of any person by name.
Which demonstrates, of course, the hateful connotation of the word in question. Railroader.
"I'm not I'm not I'm not I'm not I'm not I'm not I'm not ..."
And so on.
Well, here's where I stand. I am concerned about my players. I am anxious not to use my power as a DM to make my players feel beholden to me. I seek to control my natural, human tendencies to see an opportunity to guide my players and to resist - to the best of my abilities - that opportunity. I am human and I often fail. However, I know that to take any step to guide, ordain, channel or restrict a player's free and total agency is a wrongdoing. Not only in the game of D&D, but in any social situation. Expecting other people to play my game, or to play the game my way, or to use my position to manipulate their play in any way, ever, is wrong.
Even if I do this with the best of intentions. Even if I do this expecting that they will have a good time. Manipulation is wrong. Period. I will eschew it to the best of my ability in every game I manage.
I am sorry that others feel that certain expectations of what a DM is or what authorities a DM is granted gives them leave to act in any other way.