The only big danger of a good password manager is the fact all your passwords are stored under one.

To mitigate the risk, follow these practices:

• Use a good trusted, much preferably open-source option (for example, Vaultwarden, KeePassXC);
• Use a strong password;
• Do not EVER use the same password you use for password manager elsewhere;
• Use 2FA on both your password manager itself and all the accounts you store passwords for;
• Backup your password database in an encrypted way.

Together, these measures should save you from any trouble.

Now, why they are good:

• They can generate and store very strong passwords you would never make up, much less remember;
• You can be sure you won't forget your password;
• They are convenient and can auto-fill passwords for you.

Generally, using a password manager is considered a superior option in terms of security and availability compared to keeping your password elsewhere, including your head.