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?

Those are just specific particles floating around the brain

They said - there is no evidence. The reply hence is not supposed to be - how do you know that. The proposition begs for a counter example, in this case an evidence. Simply saying - love is non algorithmic - is not evidence, it is just another proposition that has not been proven, so it brings us no closer to an answer i am afraid.

A good example was given earlier -- will a program that searches for counterexamples to the Collatz Conjecture halt?

are you sure? If conscious experience was a computational process, could we prove or disprove that?