There's a little ego involved in songwriting and splits/credits... The fights go on all the time and the bigger you are, the nastier it can get (well, I guess more's at stake then too...). As related in the Independent UK:
...Sir Tim Rice and Lord Lloyd Webber, are another case in point. While promoting a new production of their musical Joseph, Lloyd Webber inferred that his long-term collaborator prefers to see his name take prominence on the songsheet. "Tim Rice has written great lyrics for the new song," he said. "It's wonderful to hear a new Lloyd Webber/Rice song after all this time – or Rice/Lloyd Webber as he'd prefer."
Sir Tim, however, is quick to reject the claim. "I have never insisted, no," he says. "The order on the credit has varied over the years from one to another. And, as far as Joseph is concerned, it's an 'Andrew Lloyd Webber Production'. I couldn't give a stuff."
May the Muse be with us, we long-suffering, humble song-crafters, and away with "successful" egoists... okay, so I'm (a little bit) jealous...