I can throw a ton of algorithms that no human alive can hope to decide whether they halt or not. Human minds aren't inherently good at solving halting problems and I see no reason to suggest that they can even decide whether all turing machines with number of states, say, below the number of particles in the observable universe, very much less all possible computers.

Moreover, are you sure that e.g. loving people in non-algorithmic? We can already make chatbots which pretty convincingly act as if they love people. Sure, they don't actually love anyone, they just generate text, but then, what would it mean for a system or even a human to "actually" love someone?