The problem is that some authorities are political or religious/irreligious hacks. Example?

Richard Dawkins' thoughts on Biology are compromised by writing books and giving speeches where he is giving views from the view of a militant atheist. Is his data presented in biology coming from a dogmatic place?

If someone is a supposed authority on an issue, they could have financial reasons to be an authority, like a rich televangelist or someone who writes books that strike emotions from a particular group.

The problem with logic is it ignores all real and legitimate additional details which mitigate whether it is correct or not. You're just going by if part A is true then part B must be true (or false, depending on what is being argued).

The trustworthy source, which then makes a trustworthy statement..

a) May or may not have gotten input first, which may or may not have been complete or accurate to start with

b) May have made an error in this particular case, because after all, they're still human

c) May have been coerced or paid or even brainwashed

d) May be right in 95% of the scenarios where you apply what they stated but that last 5% after a slightly closer look at the information renders that they were wrong.

It depends on the nature of the claim, and whether there's a reasonable possibility that the supposed authority miight be wrong. The problem is that we can't determine whether the possibility is reasonable or not without ourselves appealing to authority.