What can be done about password generation?

Question

Digital certificates

During registration, they made me send SMS with a password to my site (and it is too complicated, for example: x2GhQ21pz such passwords)
I wanted the users to set the password themselves. But my audience is 35-44 (men) g.
But the programmers told me they want to do it, but if the base disappears, we are not to blame.
And base about 8000 users. What programs are there that can protect the site?
There is an SSL certificate. Which ones are used by ebay, facebook, amazon? We need the same

Answer 1

but if the base disappears, we are not to blame.

Where will it disappear? How will it disappear? Make backups so you don't get lost.
The database should not contain any passwords.
http://getjump.me/en-php-the-right-way/#Hashing...

Answer 2

Well, they say it's not necessary. I have a backup they said

Answer 3

As far as I understand (and it wasn't easy), programmers believe that human-set passwords are generally simpler than machine-generated passwords. And there is.
If the user's password is brute-forced, only the user will suffer. An attacker who picks up a password will be able to use the functionality of the site with user rights (each user cannot download the entire database???).