I see the '2 degree limit' as rather like a speed limit on a road - both are set by policymakers on the basis of a number of considerations.
On the roads, the main issues are safety, fuel economy and journey time. Regarding safety, driving at 5mph under the speed limit does not automatically make the journey 'safe', and exceeding the limit by 5mph does not automatically make it 'dangerous'. Clearly, all other rings being equal, the faster one travels the greater the danger from an accident - but you also want to go fast enough to get to your destination in a reasonable time. The level of danger at any particular speed depends on many factors, such as the nature of the particular road, the condition of the car and the skill of the driver. It would be too complicated and unworkable to set individual speed limits for individual circumstances taking into account all these factors, so clear and simple general speed limits are set using judgement and experience to try to get an overall balance between advantages and disadvantages of higher speeds for the community of road users as a whole. Basically, a simple limit is practical and workable.
I see the climate policy focus on global mean temperature (eg. 2 degrees C) as playing a similar role - a simple indicator for policy purposes, and as basis for discussing pros and cons of different policy choices, but not to be taken too literally as a real threshold. Despite what we sometimes hear, there is no clear, scientifically-based threshold for 'dangerous anthropogenic climate change'. Clearly the stronger our influence on climate, the greater the risk of exposing ourselves to conditions we are not used to and hence unprepared for (eg. heavier rainfall, higher storm surges, longer or more intense heat waves). Staying below (say) 2 degrees does not mean these things won't happen, and exceeding (say) 2 degrees does not mean they'll suddenly happen all the time. Specific regional climate changes are not strongly linked to any particular level of global warming - there are many factors which affect the relationship between global mean temperature and regional climate and weather. Moreover, the level of 'danger' from such things also depends on how resilient society is - whether adequate flood provision exists, for example. There's so many complex factors that it's impossible to truly say what the 'dangerous' level of global warming is. However, a simplistic indicator based on global mean temperature does at least give some focus for discussion.