So it’s all to do with how rough the surface of ice is. Your desk is very rough at the microscopic level (which means you see it as smooth, but really, it’s got a lot of little peaks and dips in ti). This is why we can grip stuff like your desk, because of all of these little “imperfections”.
Ice is a weird one because, on its surface, it has a tiny, thin layer of liquid water. This tiny layer smoothens out all of those imperfections, which means you can’t get a grip on the surface! At least, that’s what we think is going on.
Excellent answer by Mark, can’t beat that! If you study science or engineering in university, you will solve lots of slipping problems in first year mechanics.
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