Mass extinction date set by science.

[Gawdzilla Sama]

Why should I think that our species can avoid a mass extinction? We are not that special.

We are the only known species that is aware of the potential for its own extinction, and the only known species that is capable of technologically innovating solutions to problems that might otherwise result in the extinction of a species. We have the ability to make accurate predictions about future outcomes, and if one of those potential outcomes is our extinction, then it is possible to avoid it if planned for.

*Mass extinction refers to the rapid loss of taxa across numerous genera, families, orders, classes, and phyla. So your sentence should read "Why should I think that our species can avoid extinction?"

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Until now they've rare been self-inflicted.

I don't know of any "self-inflicted" mass extinctions. 

And even among individual extinctions, I don't know of any species that inflicted an extinction upon themselves through heavy modification of their environment.

Just hang around.