I believe that there is a gap in your argument. We have to hustle to hit our Paris Agreement targets, but missing them isn't exactly equivalent to dying - at least, I don't think you've shown it to be. That's why it's not "a race for our lives".
But, you may say, a lot of people will die from climate change. (And a lot definitely die from pollution.) A lot die from malaria, too, but we don't have a "race for our lives" on that one. Cynically, most people don't consider a bunch of other people dying as a "race for our lives".
(We did more or less have a "race for our lives" on AIDS, though. It seems that we start to care when it's hitting closer to home, and we think that it could be us. That's the problem with your argument. You haven't shown people enough evidence that they think it will be them dying, so they don't think it's "a race for our lives".)
Going above Paris gets into the "there be dragons" realm of human survival. The Pentagon is predicting mass migrations, wars, famine, and economic implosion[1]. I feel like that certainly constitutes "race for our lives" level of rhetoric.
Usually, when someone balks at strong rhetoric on climate change they are (1) unaware of the scale and severity of the problem or (2) don't see those affected as within their "our" definition (e.g. it will happen to other people, not my people). The former is slowly being solved through increased education and awareness, the later will likely always be present due to human tribalism and racism.
As far as the malaria theory, it's a very different strategy when you are actively causing the problem you are trying to solve. It's as if we are repeatedly shooting ourselves in the foot, then some of us say we should stop, then you say why are you so focused on the foot-shooting vs cancer killing us. One is an immediately addressable problem caused by ourselves, one is a natural threat that is not under our direct and immediate control (thus takes much longer to understand and solve).
IIRC, Eocene period had atmospheric CO2 up to 2000 ppm, the known max. I figure we'll meet that target (ocean acidification, thawing tundra, desertification). So life will somehow survive. Though I wouldn't place bets that we humans will squeeze thru that keyhole.
But, you may say, a lot of people will die from climate change. (And a lot definitely die from pollution.) A lot die from malaria, too, but we don't have a "race for our lives" on that one. Cynically, most people don't consider a bunch of other people dying as a "race for our lives".
(We did more or less have a "race for our lives" on AIDS, though. It seems that we start to care when it's hitting closer to home, and we think that it could be us. That's the problem with your argument. You haven't shown people enough evidence that they think it will be them dying, so they don't think it's "a race for our lives".)