I think most people would not think that Taiwan is a great place to ride a bike because they don't know too much about it. To be honest, all I really knew about Taiwan before I came here was that -- at that time -- almost everything we used said "Made in Taiwan." And then if one has never been here -- and even if they have -- all one has seen or heard about Taiwan is street scenes from Taipei or the crazy. But get out of the city and there is a lot of nature out there. And with a mountain range running right down the middle, that makes for a lot of mountains roads and hilly routes to ride.
Also, if one likes flat routes instead of climbing, the roads leading to and along the coast are all flat and fairly wide. As for the traffic, it might be crazy, but outside the city it isn't too bad as the drivers are used to dealing with scooters and old people on bicycles and so they are both more tolerant of us cyclists and more aware of us.
Once again, to be honest, I didn't start cycling until I came to Taiwan and haven't done any other than here, so I can't compare the cycling here to the cycling anywhere else. But growing up in eastern Ontario I used to think some of the hills around there were pretty bad, but after seeing the hills and climbs around here, those ones around my hometown don't seem so bad when I go back.