Should the six counties belong to Ireland?

I was born in London, and moved over to Ireland with my mum and sibling when I was very small! I have been brought up to believe that the six counties belong to Ireland! My mum spent 27 years living in England and she firmly believes that the northern six counties should be a part of Ireland, I mean the island of Ireland is one landm and should be one country, right! I don't know what to believe, Irish people can tell you one story and the English another, and both can be very convincing! A friend once told me about politics, when I said I can stay in the middle and not be biased on any political matter including this one, and she told me that you have to pick a side do therefore you are always biased and that's just life? I don't know what to believe about the six counties, they should be part of Ireland? UK have enough, why do they want a measly six counties with a small population?