After a lot of research online to find an answer, I have a theory for this now - The intention of making Dumbledore offer these magical, strange, semi-sentient, toothed sweets to Harry is nothing but to show the humorous side of Dumbledore's character. The film-makers have done this at a few places in the entire series and sometimes (like in this scene) they have even added something which is not in the book itself.
This theory is a combination of 2 main points:
1) The scene happens differently in the book. (Supporting link - http://www.the-leaky-cauldron.org/features/essays/issue4/pensievethoughts/). And,
2) The film-makers (especially post Chamber of Secrets) have tried to put a little emphasis on the humorous aspect of the Dumbledore's character as evident from one of the online sources (Supporting link - https://www.academia.edu/810353/Lost_in_Translation_Harry_Potter_from_Page_to_Screen). Relevant excerpt is as follows:
A ﬁlm can, however, aspire to translate what the adapters—foremost, the director, but also the screenwriter—perceive as the novel’s core experience. Central to Dumbledore’s character is a balance between seriousness and humor. As Steve Kloves puts it, “Dumbledore bears such a tremendous dark burden ... and the only way that he can keep that at bay, the darkness, is to be whimsical and humorous.” Newell can omit Dumbledore’s wry remark about Aberforth because, as Cuarón’s ﬁlm does, Newell’s provides many examples of the headmaster’s sense of humor, restoring this aspect of his personality after its near-absence from the ﬁrst two movies. In one moment not in the novel, the fourth ﬁlm has Dumbledore telling Harry that “the licorice snaps are a wee bit sharp” (as Harry discovers, they snap at your ﬁngers if you don’t eat them promptly). When visiting Harry in his dormitory near the movie’s end, Dumbledore observes, “I never liked these curtains. Set them on ﬁre in my fourth year—by accident, of course.”