There are zero airlines offering flights to Taipei. The most direct route isn’t necessarily the cheapest – being flexible is key to finding the lowest airfare rates. For example, try searching by month to see the best time of the week to fly.
Make sure you use the search options above to search for flights to other airports in Taipei, not just Taipei Taiwan Taoyuan International (Chiang Kai Shek International) Airport. The more options you look at, the better your chance of finding a cheap deal.
If you're planning on going to Taipei during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.