Statistical Fallacy?

Bad communication. Nobody has defined "dangerous."

Person A is expressing an opinion with a subjective term.

Person B is being a bit too argumentative calling "baloney" on an opinion.

"In fact, a person who climbs a mountain in the Himalayas is safer than one who doesn't climb at all."

This is either a fact as stated, or untrue, in which case it is simply misinformation or a lie.

The first thing I noticed about this exchange: Without more context, 24 climbers dying in a year is not a terribly meaningful statistic. For evaluating how dangerous an activity is, the number of deaths (or injuries) should be normalized for the number of participants, and the duration when they're actively participating. You might see it presented as something like 0.6 deaths per 10,000 climber hours. To put it another way, 24 deaths among 500 climbers is much more concerning than 24 deaths among 250,000 climbers. And, the fact that about 5000 pedestrians are killed by cars in the US every year is a result of there being more pedestrians who, on average, spend more of their time walking. Not that walking down the sidewalk is 200 times more dangerous than climbing Everest.

As Bo mentioned, the fact that dangerous isn't defined as an issue. But also, great majority isn't a well defined term. That might mean 99.9%, that might mean 60%. But even on the high end of that, if you go on a climb that you have a 95% chance of surviving, that's still a 1 in 20 chance you'll die - odds most people wouldn't take voluntarily. So, it may be true that the majority of climbers survive their treks, but it would still be considered unsafe by most people's standards.

Now, to say that a person who climbs a mountain in the Himalayas is safer than one who doesn't climb at all, with no other support, my first inclination would be to say they just made that up. The only way I could see this being true is through some oddly specific interpretation, such as to say that climbers are habitually more careful in their day to day activities.

Is there a claim? Is the claim supported? If there is a claim and it's not supported, then it's an unsupported claim. And if an unsupported claim is considered a fallacy, then there is a fallacy. Please note that a statement can be true and still commit a logical fallacy. A fallacy lacks sufficient evidence to support the claim. Was there a claim made? An emotional and emphatic statement was made that began with the words, "In fact,..." So, there is a claim. If, by contrast, a statement is made with the qualification that it's a person's opinion or theory , then there is no direct claim of truth. Although the assumption of truth could be implied even if someone states that it's their opinion, So, the subtleties in communication can make it difficult to know what the person really intended. But in this case, most people would not question that a claim is being made, and it's not supported. Therefore, it's an unsupported claim.

It could be discussed for days about what the definition of danger is, and whether a very well prepared climber is engaging in less danger than a half awake distracted driver going to work. But that's all immaterial to the determination of whether a logical fallacy was actually committed in the question.

This is a classic case of the False Comparison fallacy, with a dash of Misleading Vividness. Person B makes it seem like all of us non-mountain climbers are just sitting ducks, waiting for tragedy to strike, while the reality is probably closer to tripping over a rogue cat on the stairs than being buried under a laughing avalanche. Person B may also be suffering from the Optimism bias, thinking those super-fit, attractive mountain climbers simply have immunity to mortal danger like they do to doughnuts. The probability of dying from inactivity or a climbing accident isn't as cut and dried as Person B is making it out to be. It's like saying eating a hotdog at a baseball game is more dangerous than swimming with hungry sharks because more people choke on hotdogs each year. What's next, Person B - insisting that skydiving is safer than cooking because more people get burned in the kitchen than hitting the ground at terminal velocity? Nice try!