This is one of the things which we like to say about startups, but it doesn't stand up under scrutiny.
The competing job offer is Google or another megacorp. What's their turnover for engineers in a year? 10%? 15%? The definitionally average startup has a higher turnover even if we restrict it to turnover caused by business failure, to say nothing of voluntarily or involuntarily losing one's job.
If you exit a position with Google/etc, you have a network full of people who also spent the last couple of years at Google. You can easily lateral into jobs of comparable quality. If you exit a position with a failed startup, your lateral transfer is likely into another job which pays below market. Your immediate professional peers are also people trying to avoid the failure stigma. They may also be slightly busy looking for a job to help you with your own job search.
If you work for Google for 2 years and then separate from them, your 401k increased by $30k in the interim and you probably have six figures sitting in the bank account. If your startup is shot out from under you, you may end up counting the number of ramen boxes in the pantry while hoping that the startup can make good on its final payroll check.
If you work for a megacorp and are let go, it is highly likely that you were let go for firm- or individual-specific reasons rather than industry-wide calamity. This is very much not guaranteed in startups, where e.g. ebbs and flows of the capital market can cause a daisy cutter to hit the hiring pipelines at dozens of firms at once. You could lose your job at the same time that everyone else stops hiring. Ask the wizened veterans of the dot com bust who are, what, in their late 30s?
Startups are meaningfully less secure than working at bigco. Anyone who says differently either doesn't understand them or is trying to sell you something.