I'm a sceptic about the dangers of population decline. The benefits seem obvious: the world has limited resources, a lower population can make these resources go further. After all the world's population can't expand indefinitely. The supposed dangers on the other hand seem unconvincing. For example, many people worry that an increase in the proportion of the population that is elderly will strain government budgets. True, but children also consume more wealth than they create, so the money people and the government spent on children can be diverted to caring for the elderly.
Which brings me to this. I think it's a poor article, because the author doesn't really establish a clear link between the problems he describes (low birth rates, brain drain) and his solution (allowing Chinese students to come to Taiwan). But I'll ignore that issue and pretend the author made a more common, cogent argument, namely that Taiwan's schools need students or they will be forced to close. The problem with this is that Taiwan's schools are government-subsidized- even private colleges. Closing schools will free up money that can be used to help the elderly. Allowing Chinese students in is basically spending Taiwan's limited public resources on Chinese students (unless their tuition covers the full costs of their education here). The author argues that allowing Chinese students into Taiwan will make them more friendly to Taiwan, but only offers one example. To me it is far from clear that the supposed benefits outweigh the drawbacks.
Taiwan arguably has too many colleges as it is- Taiwanese people often comment on how easy it is to get a degree these days, since there's so many colleges that anyone can get into one. That may sound nice, but not everyone needs to go to college, and in a world of limited resources not everyone should be granted a subsidized college education. A final issue many people bring up is teachers- what will they do if they don't have students? One solution is smaller classes. Another is retraining to care for the elderly.