Hilary Putnam was a strong proponent of functionalism.
The strongest arguments for functionalism stem from the weaknesses of the competing mind-body solutions. Putnam, for example, believed materialism was too narrow in its scope. The idea that mental states could be reduced solely to physical occurrences lead to the emergence of a one-to-one relation between the two; we feel pain due to c-fibre stimulation, and nothing else. X causes Y. Without X, Y does not occur.
This, Putnam argued, couldn’t be true. We know that cats, dogs, reptiles, birds, and molluscs feel pain. But this does not mean that they have brains like ours. This lead Putnam to speculate that the relationship between our mental states and physical activities in the brain do not have a one-to-one relationship but can be multiply realised from many stimuli. The multiple realization aspect of functionalism has drawn many to favour functionalism over materialist positions.
Qualia Functionalism cannot explain the qualia phenomenon, also known as “what it is like” to have a mental state or an experience. In characterising mental states in causal terms, there is no room to characterise the feeling behind mental states. Someone who sees greens instead of reds might still respond to the stimulus of red in the same way as someone who sees the red. However, their qualia- or the feeling behind the experience- would be wildly different.
Other mind-body explanations have been disproved. Therefore, this must be the correct explanation.
Just because others do not offer a comprehensive explanation doesn't mean functionalism does.