Why isn't Northern Ireland part of the Republic of Ireland today?

Because its part of the United Kingdom............

Blacks all over there

It is all part of a scam from Pakistani marriage scams. Ignore lonely Orla

Go read the history of the relationship between the UK and Ireland. It's complicated. 

The British colonised what now Northern Ireland won't give back to appease the Protestant Scottish and English settlers who threaten  to murder Roman Catholics if there is United Ireland like they did in 1912 and again start the troubles in 1968.

Brits out, TAL 32

Because there is an organisation in Northern Ireland which has promised a 'no warning' bombing campaign in the South, if the taigs show signs of forgetting what they have been told.

Because those who lived in the majority of Ulster decided they wished to remain British and not leave the UK, while Ireland decided they wished to become a free state100yrs ago and then later the republic and they still wish to remain part of the UK

Prior to 1922, all of Ireland was part of the United Kingdom.  The South wanted to leave: the North wanted to remain.  The United Kingdom do not intend to throw Northern Ireland out against the will of the people.

There's a WHOLE load of history around this. Do some research; it's on Wikipedia for a start.