They have a saying in leadership: Never show them fear.
A leader must be a piller of unwavering confidence, must always know what they are saying and must stand behind their decisions. Players must never even think to question a ruling.
In a perfect world.
But we are not in a perfect world, are we? Nowadays, players know just as much and often there'll be that one player that most definitely thinks they know more than the GM.. at least about some sideline aspect of a game or game world.
A GM must be Enlightened ∞
Yes, this is a loaded phrase. Let's just say that a GM's decisions must feel right to all players. This means that a decision or comment must be timely and appropriate. When the GM speaks, it must captivate and breed agreement.
How? The GM must not be wishy washy. Unless it becomes blatantly incorrect in the eyes of the hidden mechanics of the world, a decision must be stood by.
"Aww, but how come I missed? I was using my +3 arrow?"
Herein is the strong indication of a whiney player. Do not buckle! Plainly state that they simply missed. It happens. You do not need to justify it. If this is a rules lawyer, perhaps you could hint at some sort of wind thing, or help their minds run free with fears of damage reducing supermonsters or regeneration, or whatever misinformation you feel like tormenting them with.
If you feel guilty about not buckling to a complainer, make up for it in subtle ways. Over time, you will learn the skill of reading the signs and can avoid such circumstances entirely.
A ruling must never seem arbitrary ∞
The players rely on a GM to be their guide. A GM's decision must seem neither idle nor arbitrary.
This may be accomplished by standing by a rule.