That reason is rubbish. There will not be any significant number of people on Mars before 2100, maybe two or four at a time. That will not prevent any extinction.
So, because it will take time to develop a sustainable population off planet we shouldn't do it? We don't know when the next ELE event will be; it could be an undetected space rock which will hit us next week, or possibly Yellowstone erupting in a thousand years. I don't know when the next century flood will happen, so I should spend 5 years preparing my family for such an event.
Besides, the human musculoskeletal system can not properly develop nor even be maintained on Mars. The rocky world with sufficient gravity for that is Venus, and it has a few wee little problems regarding human habitation, for instance even living in balloons at altitude where pressure and temperature wouldn't kill has sulphuric acid rain.
Our skeletons will develop for the level of gravity where we live. A human born and raised on the moon will have enough strength and muscle to live normally on the moon. Same deal with Mars. Your argument comes into play for returning to earth, where it will take some time to strengthen the bones and get used to our gravity. It is unlikely to cause immediate death.
Venus' gravity, temperature, and acid rain are irrelevant to this discussion, and only serve as a straw man.