This...is because one party to the relationship (business or personal),is always invested more in the relationship than the other; and that party has either not seen the rift coming, or not wanted to see it...the latter being far more the case. The change is resisted, in the hope of maintaining the status quo....not realizing that the status quo, now, is a position where one of the two people wants out! So an untenable peace prevails for some time, until it slowly sinks in that one party is, indeed, serious about moving on, and the "divorce" finally happens.
In personal relationships (it can't, obviously, be done with professional ones), some people handle this by just cutting and running....which, I feel, is the most dreadful way of doing things. It may spare the party of the first part a lot of grief...but to the second person, the burden of grief is much greater. Being left suddenly, often with no clue what has happened, and why....no person of sensibility, or sense, could do this to another person with whom they've been friends (or more) ...but...they often do! All the good times that two people have had, are left stranded on the rocks of the abrupt way of parting, and no good feelings are possible.
Timing a "moving out" announcement, and managing the process of disengagement, is a very tricky task, indeed, and calls for a lot of maturity on the part of the announcer. If handled with tact and consistent diplomacy, the parting can be very amicable and the relationship is not completely broken off, but continues on different lines.
But most often, this just does not happen. The shock of the resignation (from the job or the relationship!), the feelings that are aroused by the thought of the parting...all serve to vitiate the parting, and make it a difficult time for both people. If official partings can become so emotional (when KM resigned from one job, he called his boss to give him his decision, and the next morning, the boss' angry wife called him up to say that the boss had not slept a wink the entire night...why did he upset him like that? she asked.)...I can just imagine how difficult it must be, for example, when a married son and his wife want to move out of the parental home..in a culture like ours, it would be viewed as nothing short of insulting the parents. Wanting a different level of relationship is equated to wanting no relationship at all. Recriminations follow, pressure is applied...and it's all one can do not to back down from one's decision...and sometimes, indeed, one does succumb.
But, in my opinion, nothing is really gained by backing down. A decision to move on, whether professionally or personally, must be taken in a considered and rational way (not in the heat of emotion, job stress or other pressures) and once taken, should be adhered to. I remember reading a wonderful dOhA (couplet) by either Kabir or Rahim...to the effect that a broken string may be repaired, but the knot is now there for ever....so too, with such decisions. Once one has taken the decision to carry on....one must take the consequences of that decision, and go ahead with it, no matter what the storms may be, that one has to face.