The choice between the gerund and the infinitive in a certain construction

I am pretty much sure that for native speakers the issue I am going to bring up might look as an uncalled question as they can easily figure out which form of a verbal part of speech should be used, be it a gerund, an infinitive, or a bare infinitive. However, it can be pretty much misleading for a foreigner because the same construction works differently with different words and I don’t see a logical explanation. For example:

1. The purpose of this article is to analyze the issue…



2. My hobby is reading.

   
   
   
   

   One may assume, and many foreigners really come to this conclusion, that it’s OK to switch the “gerund” and “infinitive” as the meaning will stay the same, that is:




3. The purpose of this article is analyzing the issue… (same as 1 above)



4. My hobby is to read. (same as 2 above)

However, as I was told, this assumption is erroneous.

Another example:
His task was watching after them. (not good)
His task was to watch after them.

Is there any principle which governs the choice of the right form in such cases?