Final answer:
Thetis and Peleus did not invite Eris to their wedding because she was the goddess of discord, and they feared she would cause trouble at their celebration.
Step-by-step explanation:
The reason Thetis and Peleus refused to invite Eris to their wedding is because she was the goddess of discord and would likely spoil the festivities. Eris was well-known for causing strife and turmoil, and as such, her presence at a joyous occasion like a wedding would have been considered highly undesirable. This decision ultimately led to the events of the Trojan War, as Eris, in her anger for not being invited, threw the golden apple of discord among the guests, which was labeled "for the fairest" – sparking jealousy and conflict among the goddesses.