If I dont have google account and dont want one I cant start program, why not?
You can sign in using any email address and a password. Simply type it in while logging in and you won't need to use your Google Account.
However, if you've used the "Sign up using a Google Account" option, please use the "Log in with Google Account" when you want to log in. Then, you can set a new Todoist password in Settings (gear icon in top-right corner) -> Account to use it in he future.