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?

Solution 1:

(1) There is a grammatical / semantic term applied to verbs, semelfactive - occurring but a single time. This is the case with The purpose of this article is to analyze the issue but not with My hobby is reading, where a continuous aspect is obviously applicable. Contrast My intention is to read after supper.

(2) Many verbs catenate

(Appendix:English catenative verbs - Wiktionary) and take the bare infinitive, the to-infinitive, or the -ing form rather unpredictably (the article contains a useful list). Sometimes, the meanings differ:

I forgot to visit Aunt Molly. (I'll have to go next week instead.)

I forgot visiting Aunt Molly. (She reminded me that I had when she phoned yesterday.)