Fights: As you have shared your facebook or mail id password with your partner, he/she would check suddenly or everyday and one mistake can lead to big fights. Basically, small issues leads to fights among couples.
More doubts: As your partner is keeping an eye on you, doubts can increase more. Your partner spy on you because he/she has a doubt on your loyalty. Even if you give your facebook password, the doubts will not reduce but gradually increase.
Misconceptions: If your message is taken wrong, it can lead to misconceptions with your partner. Even after explaining the exact situation, the doubts on your partner's might can reduce for the time being but won't stop him/her from spying on you.
Lack of privacy: If you are sharing your password with your partner, you lose your privacy. Best termed as space in relationships, the lack of privacy can become really frustrating at times. There are few things which you would like to share with your friends and not partner. This lack of space between friendship and love relationship can become an irritation.
Sharing your facebook or mail id passwords can only lead to misunderstandings and conflicts. You might think you are right and don;'t mind sharing your password with your partner but the spy attitude can become dangerous in the healthy love relationship!