Is it really absolutely out of reality to use "liking" and "loving"?
No.
Despite what some teachers think (having been taught that 'verbs of emotion' are never used in progressive forms), it's normal and natural. If 'like' and 'love', and similar synonyms and antonyms) refer to a deep, lasting, emotional attachment, (or lack of it) then of course the feelings are not seen as being of limited duration, and progressive forms are unlikely. However, if we use those verbs to mean something like 'enjoy' then a progressive form is natural.
I love (living in) Prague, but I am loving (being in) Berlin (this weekend).
In the (probably anachronistic) quote I gave from the film, the speaker is explicitly stating that his not liking of 'him' (Billy the Kid) is of limited duration. Long term, the speaker likes Billy. Short term, he is either in a limited time of dislike, or he is in a time of beginning of dislike.