Intuitions do most of the heavy lifting
Philosophers often argue for particular positions:
The existence of free will
The existence of qualia and the legitimacy of the hard problem
Moral realism
...and so on by both:
(a) appeals to intuition, and related clusters of views, e.g., claims that the views in question are necessary, obvious, self-evident, Moorean appeals, and so on.
(b) a variety of other arguments, intuition pumps, thought experiments, and so on (e.g. Mary’s room, moral convergence, etc.)
However, I suspect that if you convinced proponents of these views that none of the arguments in (b) worked, many (perhaps most) would still endorse the view. However, if they somehow abandoned (a), I suspect most would stop endorsing the view (or at least stop caring as much about it).
Functionally, aside from appeals to intuition (and related appeals), positive arguments for these views strike me as largely dialectically superfluous. I think they almost never convince anyone, and almost never serve to sustain their proponent’s beliefs in the face of counterarguments.
Take away all the arguments for moral realism other than appeals to one’s intuitions (and related appeals), and I think many realists would maintain their views. Reverse this, and I think the motivation to sustain a belief in moral realism would, at least for many, largely dissipate, and. At the very least, I suspect the view would be held with far less enthusiasm, largely fading into the background.
I have no way to prove this, and this is mostly a bit of speculation on my part, but I think it’s probably right, and I think that’s important. I think it suggests that arguments aren’t really doing much work in philosophy. That isn’t to say nobody ever changes their minds in response to arguments… I just think that’s the exception, rather than the rule.