Why is it that getting a Phd in Europe or US if you are a non EU/ non Us CITIZEN IS SO DIFFICULT . FOR HEAVEN'S SAKE I EVEN HAVE MY OWN FUNDING.

Its fairly unusual for a Uni not to take you on if you are willing to fund yourself; has anyone you have applied to given you an indication why you have not been successful? It also depends to an extent on your discipline - if you are in pure science do you have enough to cover lab costs and materials etc?

I have funding for my fees and cost of living

which countries are you looking at? i definitely know that in quite a few countries in europe professors are more than happy to take you on, if you have your own funding. have you looked at countries without tuition fees (i guess in Britain it could be a problem). what field are you in?