Why would it be faster to beam information up to LEO and down than use optic fiber or microwave link?
Because through space and the atmosphere the radio waves and the laser beams Starlink uses are propagating at over 99.9% of the speed of light, and in a straight line between the satellites, through very few 'hops'.
Fiber optic cables on the other hand only run at about 68% speed of light, and they also have a lot more 'hops' typically to boost the signal but also to route around physical geographical features.
Note that for example
New York to Frankfurt ping times over fiber optics are 96 milliseconds: that's 28,800 km at the speed of light round-trip. The two cities are only 12,400 km round-trip apart when taking the curvature of Earth into account - which means that even in practice fiber optical networks between two of the largest financial centers of the world are very sub-optimal. The distance of bouncing up 400-600 km to LEO distance is a minor cost of latency: the path of photons will still be well below 20,000 km and the LEO communications latency will beat the fiber optical latency.
If we go further down the hierarchy of geolocational advantages then things get progressively worse: it's not uncommon to see fiber optical pathways several times the length of the true distance between two cities or countries (!). If we check the global topology of undersea fiber optical cables:
Some places are very far off the beaten path of the Internet, and for example there's no direct routes from Asia to Europe or from Australia to Europe. There are very few straight lines - which adds extra hops and distance to over the ~30% slowdown that light moving in Corning glass already causes.
Now as destinations get closer to each other the latency of fiber optical networks improves: so for example two cities that are 100 km apart usually are going to have better latencies than LEO constellation - except if the Internet backbone center of the country is hundred of kms away, which is frequently the case.
Not to mention the incremental cost: a single intercontinental cable takes years to plan, lay and costs hundreds of millions of dollars overall. A LEO constellation connects everyone to everyone within the constellation's latitude limits.
But in terms of global backbone of Internet traffic, a LEO constellation is superior in almost every regard to fiber optical networks, and they are much easier and lower cost to scale up in capacity as well - so they will almost certainly win the race for more and more bandwidth.