Although there is a certain level of risk involved in jump starting a car, you can minimize it to almost nothing if you follow the correct procedures.
Of course, there are a few instances where jump starting really is a bad idea. For instance, many hybrid vehicles have a 12 volt “auxiliary” battery that can be jump started if it goes dead, but attempting to provide a jump start from it may drain it to the point where the vehicle won’t start. If you drive a hybrid, that may be why you were told that it’s not “safe” to jump start your car.
There is another potential jump starting issue that’s associated with vehicles that have batteries that are difficult to access. Some of these vehicles have a remote positive charge/jump start terminal, and others require you to do some work to access the battery. In cases where a remote terminal isn’t available, it’s typically a bad idea (and potentially even unsafe) to jump the vehicle by using the positive terminal on the fuse box, or any other connection that isn’t actually the battery.
As far as portable car jump starters are concerned, they’re perfectly safe with the one caveat that you still have to follow all of the correct procedures.
You still need to hook a car jump starter up in the right order and in the right places, and you can only use one to jump start a traditional car battery or the auxiliary 12V battery in a hybrid, but not the high voltage batteries in a hybrid. Of course, using a jump box presents a unique danger in that you have to be careful about where you set the device while it's hooked up.