What is the difference in meaning when the catenative verb “like” is followed by an infinitive, or by a gerund? For example:
Do you like ski jumping?
vs.
Do you like to ski jump?
Also, what is the difference between:
My brother taught me to read and write.
vs.
My brother taught me reading and writing.
I would suggest that there might be a subtle difference between "I like ski jumping" and "I like to ski jump" insofar as the first conveys a general liking, similar to "I like to watch the sport of ski jumping," while the second seems more specifically engaging, similar to "I like to ski jump on the Matterhorn on clear Sunday mornings."
I think "I like ski jumping" is more ambiguous in terms of whether "I myself" actually engage in the ski jumping activity, where "I like to ski jump" pretty definitively means that "I" am the one who is ski jumping.
In TEFL we teach that there is a subtle difference between, for example: I like to go to the dentist's every six months and I like going to the dentist's every six months. The first, with the infinitive, suggests that I think it's a good idea, whereas the second, with the gerund, suggests that I like the experience.
I'm not sure you can generalise among verbs.
For "like", I think there is no difference in meaning, but I find "like ski jumping" far more natural than "like to ski jump"; however, I have an impression that "like to" is more common in US English .
For "teach", there is a difference: "teach somebody to read and write" implies the imparting of those skills from the start; "teach somebody reading and writing" implies the two things regarded as subjects to be taught, and might include things like calligraphy or reading comprehension (though "reading and writing" will pragmatically suggest the basic skills). There will not necessarily be a difference in the events described by the two phrases, but if there is not, the focus is still different.
Just to complement Colin’s answer, I was taught that “I like to ski jump” is indeed more common in American English, and “I like ski jumping” in British English.
Related to this topic, I recommend this topic on Stack Exchange and this answer on the English-Test forum.
