Your argument starts with the premise that we begin with full information. I think that in those situations sufficiently complex enough to be interesting, knowing full information is virtually impossible. What we actually do is work from a position of sufficient information, but sufficiency is a judgement call and may be in error. So we don't have a full grasp of reality, but only a partial one.

And, logic and reasoning while theoretically capable of being perfectly performed are also capable of error, especially if there are many complex factors to be considered. The fact that it can theoretically be done doesn't mean that it has done in any case.

The "world is flat" argument has been used in a number of discussions of a example of the efficacy of working with imperfect information.

Why do I think we can't perceive reality objectively? We have sense organs, they have limitations. For example we believe objects are solid although physics tells us they are almost completely empty. In fact there is some question if anything in there is solid but that goes beyond my level of physics.

So the idea that we are dealing with solid objects is one of those examples of imperfect information that we deal with routinely.

To be clear, the fact that the world is real and that we are capable of perceiving it to some degree and using reason to analyze it means that there is always a right answer to be found. I just don't think that we are usually in possession of it, only successively better approximations.