Like in the following example:
I would really appreciate having some feedback on this topic.
Why can’t I just write “to have” instead of “having”? In this case, they are not supposed to be interchangeable, but why?
I am afraid that, as the EngVid page on Gerunds and Infinitives listed by FumbleFingers says, this is simply an arbitrary rule of usage.
I disagree with a few of the statements on the page. but I agree with its general point nd with most of the specific classifications given there, and i can't advance any systematic criterion for which verbs take an infinitive, which take a gerund, and which can take either. Perhaps there is something in the history of the words or their earlier forms which would make a pattern here.
On specific verbs, the page lists "abhor" as requiring a gerund ("He abhors playing soccer.") but I think it can also, albeit less commonly take an infinitive ("He abhors to use the passive voice.")
"Appear" in the sense "seem to" takes an infinitive "This appears to be a rule without a reason.") but in the sense of "shows up" or "becomes visible" can take a gerund. ("At the start of the show, she appears playing a saxophone in a green costume." "In Hamlet the ghost appears walking the battlements of the castle.")
"Chance" is listed as taking an infinitive, but such a sentence as "I can't chance leaving the problem unsolved." seems perfectly natural to me.
Other disputes over the exact rule for a given verb might be made, but the basic fact is that the rule is specific for each individual verb.