The 4th amendment is intended to ensure (among other things) that the government can't search some locations for evidence without first proving they have a good cause for that search.

The 5th amendment is intended to ensure (among other things) that the government can't use force or threats to make you admit to a crime, regardless of if you committed or didn't commit that crime.

The distinction is that a court could grant the right to force someone to put their thumb on a phone, or look at a phone's camera, but they (in some but not all cases) cannot force you to type in your passcode.

The argument is that your fingerprint or face is not "testimony" but a fact of who you are, but your passcode is a testimony, a declaration that you have some specific knowledge.

A phone unlocking is equivalent to it saying "Yes that is my owner/user", and that is not that person testifying, it is the device testifying against that person. Similarly it would be as if someone kept a picture of them committing a crime that was found with a valid warrant, they could not claim that having taken the picture it is their own testimony and can't be used against them. Taking the picture is a past event and requires no compelling of testimony to be used as evidence.

Getting biometrics without a warrant is a contentious issue. There are situations where a warrant is not needed, and these have also been abused to gather biometrics in situations that should have required a warrant but it was denied.

But it's easy to trick the user. Very easy. And because passwords tend to be difficult to use, users tend to pick easy ones, such that you don't need to trick the user at all. With bio, the user may opt to have the protection whereas with password they either may not, or it may be trivially bypassed. Bio systems can be engineered to be anti-phishing, anti-MITM, etc. Incredibly hard to do that with passwords.

By claiming that the user has to do something to use a password ignores the vast, vast set of vulnerabilities involved.

One is not really better than the other per se. It's very use case dependent and you optimize for a specific outcome based on the risks at hand. You won't perfectly get every possibility nailed.

What about voice- or movement-based biometrics? (These are just the first counter-examples that came to mind.)

But to your point, those require doing, which is the difference. Regular use in mixed environments (airport terminal, office, waiting for the train, etc.) is TBD. As long as I have a password backup for the days I’m in bed sick.

https://youtu.be/-zVgWpVXb64