Of course it is our business who the US President is - decisions made in the US affect the whole world, socially, militarily and economically.
As CNN reported in 2012, "the United states has active duty military troops stationed in nearly 150 countries". The 2008 financial crash is largely accepted as being triggered by the US sub prime mortgage crisis. It is a fact that creeping Americanisation is increasingly found in many countries, including Britain.
Apart from all that, when a country as powerful as America is led by a man who seems intent on causing hatred and division, I feel it is everybody's business.