原句的确有歧义,如果想彻底避免歧义,可以：
1、改用强调句：It was not because I was afraid that I didn't go.
2、改为并列句：I didn't go,and that's not because I was afraid.
3、改为定语从句：I didn't go,which had nothing to do with fear.
4、改为主语从句：That I didn't go was not because I was afraid.
5、更换语序：Fear was not the reason why I didn't go.