Because logging out would strand you, and we would rather be missing a button than break your account.
Finoha accounts start anonymously and there is no password-based sign-in screen. If we gave you a Log Out button today, tapping it would drop you into a brand new, empty account — with no way back to the one you just left, even if you had added an email address. Your streak, your progress and your portfolio would still exist, and you would have no route to them.
A button that silently loses your account is worse than no button, so it is not there yet. It arrives when a proper sign-in screen does.
If you need to hand the device to someone else, use a private/incognito window for them, or a different browser profile. That leaves your account untouched.