Like, love, dislike and hate

In most reliable school coursebooks we find the rule that like, hate etc are followed by a gerund to say we enjoy or don’t enjoy something (ex. I like swimming = Mi piace nuotare). However,  we can also use I like, hate etc + to-infinitive (ex. I hate to keep people waiting). What’s the difference in meaning? I’m a teacher and I’m struggling how to make it clear to my students. Thank you! Best regards. Giusi

The fact of the matter is that English grammar is far more flexible than most Italians think! OK, there are some subtle differences. With “to hate” for example, “I hate going to the dentist” is generic, whereas “I hate to say this, but you’re wrong!” refers to a specific situation. But the English themselves are less obsessed with (and less knowledgeable about) grammar than the Italians and they probably wouldn’t even notice if you mixed up the two.
Honestly, if you want to help your students in life, it’s far more important that they actually learn to speak and listen to English. This is far more useful than learning grammar rules off by heart.