Positive and Negative present deduction (should, must, have to)

For the second scenario, we can also say "they couldn't hate me" as well because "couldn't" is also used to express a deduction. But, when we use "must", "can't" or "couldn't" to express a deduction for an event in the simple present tense, the meaning may be confusing if the context is not clear, so it is better to say them in different ways such as "I think they like me", "it seems they like me", "I don't think they hate me" or "it doesn't seem they hate me" just to prevent any confusion with the duty/obligation meaning or the ability meaning.