She had to go back in time. All the events that InuYasha and company went through happened in Kagome's past; if she didn't travel back in time then the events could have changed her world. (An example of this is if she didn't go back in time, there's a chance that Naraku would still be alive in her time; which would change her history.) Time travel sure does work in a strange way.
Well the first time she goes back is an accident and she doesn't know how to return. Afterwards it is because of love/friendship/sense of responsibility because by then she knows the people there and no matter how much she argues with InuYasha she likes him (well, clearly)