It's simply because they're round numbers relating to the significant fractions of an hour.
The important thing to remember about fire resistance ratings is they have precisely nothing to do with predicting how long something will last in a 'real' fire - they're simply how long the element lasts if you subject it to the furnace conditions mandated in the test standard(s). The furnace time/temperature curve looks very little like any real fire that would be likely to occur - it's pretty much what you get if you pump a constant amount of heat into an insulated metal box. That's why engineers who try and use fire resistance ratings in their ASET/RSET calculations are simply demonstrating their lack of knowledge of the basis of the tests - despite the fact that almost every fire resistance test report will include a statement that the results don't indicate the element's likely performance in a real fire!
The ratings are therefore a means of ranking the expected performance in a fire - you don't know how long these things will last, but you know with a reasonable degree of certainty that a 60-minute fire resisting structure will last longer than a 30-minute F/R structure (floor, wall, door, whatever). Our 'code' writers therefore make decision as to how important they think an element is in a fire, and correspond that with a place in the ranking (30, 60, 90, 120, 180 etc...). Insurers do the same, but generally with higher ratings.
It's a bit more scientific than my trite explanation - there has been research done to relate fire load to expected structural fire resistance performance, for elements with a known test rating, and it has demonstrated that using the above methodology will tend to give you a 'safe' design, for the most common types of building element and fire load density. There's also the fact that every country in the World who has a building code uses the same methodology (and pretty much the same test regime, with the exception of some specialist applications like offshore & road tunnels), & it seems to work!