The question is basically whether reading has anything to do with becoming myopic. The association between myopia (nearsightedness or shortsightedness) and reading has been known for at least two hundred years. During that time it has become accepted by many that the relationship is such that reading causes myopia. The problem is that multiple studies have not been able to prove that cause and effect. The relationship remains an association, meaning that they happen at the same time: people who are nearsighted are often people who read. But that doesn't prove that one causes the other. Several studies have found that the relationship is actually fairly weak. The reason it has been, and remains, a controversial topic is that statistically it is difficult to separate out different factors.
Many scientific studies of health issues start by identifying what are termed risk factors. A risk factor is something that happens at the same time as the problem being studied. Since a lot of people who become nearsighted also read, reading is considered a risk factor for the development of myopia. Determining why it is a risk factor is the real challenge. It might be that people who become myopic and people who read both do something else that creates myopia. The goal is to identify the underlying mechanism and test the theory in controlled studies.
Some different facts are useful to understand the issue. Myopic parents have myopic children more often than non-myopic parents. Children of myopic parents and children of non-myopic parents read about the same amount. So we can't say that myopic parents make their children myopic by having them read more.
The amount of time spent reading does not predict, by itself, the future development of myopia. By itself, children who read more are not more likely to become myopic. If other factors are removed, such as parental myopia, level of education, socioeconomic class and time spent outdoors, then the amount of time spent reading does not matter. It just can't be proven. Read the research.
At the present time we can't say that reading, by itself, causes myopia. But there are some studies indicating that inaccurate (under) focusing while reading (called a lag) is a risk factor for myopia development although glasses to reduce the lag were only mildly effective in reducing progression. Still, a pair of bifocals or progressive reading lens glasses has a benefit for those who have a greater lag and also an esophoria (a tendency for the eyes to cross).
Much still remains to be determined about reading and myopia development. At this time specialized glasses may be of some limited benefit, but there is no evidence that near work should be avoided to prevent the development of myopia.