This question was raised earlier and of course I don't know because I am not close to government. But my guess is for two reasons: Mainly because in theory it makes the UK a more attractive place for high earners to want to base themselves and pay tax. So an incentive for inward investment in much the same way as the corporation tax cut. And secondly because it fits with Tory ideology of low taxes. They can't afford to cut the basic rate much because so many people pay it and there is no "upside" in terms of greater compliance, i.e. everyone is on PAYE anyway. IIRC less than 1% were paying the 45% rate, so they could afford to cut that more deeply, AND as I say it might not cost anything at all if we get more people paying it as we did when we cut from 50p to 45p
BUT, and its a huge BUT, I really do think it was an utterly stupid thing to do. It looks terrible even if it costs us nothing.