Learn English – in order to [gerund] or [infinitive]

(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.)

Unfortunately, the linked answer is very vague, and not correct. It does point out correctly that gerunds are more common as subjects than infinitives. But it certainly doesn't provide any rule that works.

The British Council is right. It depends on the predicate in every case, and often both are OK.

The examples given are both correct, and illustrate a difference between infinitives and gerunds:

• My dream is to become a doctor.
  (to become a doctor describes a punctual result, with a changed situation as an outcome)
• My hobby is listening to music.
  (listening to music describes a generic durative activity, an experiential event)

Infinitives are more complex than gerunds, and they roughly point to different kinds of clause:

As McCawley 1998 puts it (p.126) Roughly speaking,
• that-complements correspond to propositions
• for-to complements [infinitives] correspond to situation types
• 's-ing complements [gerunds] correspond to events

This is the reason why infinitives are less common as subjects. Events are causes, and causes are old information; situations are normally results, and therefore new information. And the English sentence normally presents the old information first and the new information last. That's not a grammatical rule -- it's just the usual tendency.

And in this case, note how the sentences fare when reversed:

• ??To become a doctor is my dream.
• Listening to music is my hobby.

The predicate be X's dream here refers to X's personal desire for a particular situation, rather than an activity that X participates in. The opposite is true for the predicate be X's hobby, which specifies an activity, but no result. So the infinitive is uncomfortable as a subject in the first sentence -- it's result, not cause; but the gerund is fine.