Suspicion leads to distrust, which can kill a relationship. If one partner becomes suspicious of the other, it is important to discuss the reason for the suspicion as well as dispel any reason for it. If this is not done early, then it can continue to grow into jealousy or even a strong dislike for a partner.
It does not matter if your spouse cheats on you or not as long as you are suspicious that it has happened. Once you reach that point you no longer have trust in your partner. Once trust is gone the relationship is essentially ruined. It can easily cause the relationship to end.