When you are taking off, you have a short portion of the runway which you can use to abort the takeoff depending on failures, but that portion can become even shorter depending on the length of the runway.
Usually the first part of takeoff you would abort for almost any reason, and the second part you would only abort in a serious emergency, once you reach a certain point you simply cannot afford to abort because you will not stop in time to crash into whatever is at the end of the runway at which point you must take-off even if you are going to immediately request an emergency landing afterwards.
So if you are heavily loaded, with a lot of people on board, and you do an intersection takeoff, you are taking a risk that if you made a mistake or something goes wrong you will not have the ability to safely recover. That's why it's a terrible practice in this case. All it does is save a little bit of time which would be spent taxiing to the actual start of the runway.