the earlier you show up, the more likely you are to actually make your flight. But, showing up early also involves a cost in the form of time spent at the airport rather than elsewhere.
Business Insider reviews the theory behind 'How Not To Be Wrong' when it comes to airports.
The assumption is that it's 5 times as annoying to be missing your flight than spending idle time at the airport, but you could alter that to your personal levels.
if you get to the airport two hours early, you lose 20 utils from your waiting time, but the expected loss from missing the plane is just 1% × 50 = 0.5, for a total expected loss of 20.5 utils.
This is a much worse expected loss than getting to the airport an hour early. Even though the odds of missing your flight drop quite a bit, the extra time stuck in the airport creates a cost that outweighs the benefit of those reduced odds. You're better off taking that slightly higher risk of missing your flight.
I'll let you read the entirety of the explanation.
The level of stress is not addressed here—some people just like to have time ahead. And the assumption clearly comes from someone spending time in US airports. You know, those big dull boxes (and ugly, and empty, and dull, and ugly, and... you got my grip). Spend anytime at Changi for instance and you might alter the level of "annoyance".
Me? I love airports. It's part of the trip. I enjoy arriving early (granted, I've got access to tons of lounges).