Don John spoiled the wedding because he was bitter and wanted to make his brother look bad. He was the illegitimate brother, you see. Don Pedro was the legitimate brother. Don John wanted to make trouble for his guests. He had nothing against Claudio and Hero personally. Hero's father Leonato was the governor, so ruining the wedding made Don Pedro look very, very bad.
Don John is a bitter and angry person. He embraces this, and decides to take revenge on his brother and be the bad guy. He seems to revel in it.
I cannot hide
what I am: I must be sad when I have cause and smile
at no man's jests, eat when I have stomach and wait
for no man's leisure, sleep when I am drowsy and
tend on no man's business, laugh when I am merry and
claw no man in his humour. (Act 1, Scene 3)
Don John, as the illegitimate son, is not happy. He seeks ways to make other people unhappy. If he can make his brother unhappy, he will be happier.
Don John's plan was cold and calculating. He arranged for Claudio to see Margaret having sexual relations with Borachio and told him it was Hero and another man. Claudio flipped. He believed everything and renounced Hero on their wedding day.
The saddest thing about this is that as bad as Don John's actions are, Claudio's are also horrid. Claudio waits until the wedding, then refuses to marry Hero. Leonato demands proof that his daughter was unfaithful.
What do you mean, my lord?
Not to be married,
Not to knit my soul to an approved wanton.
Dear my lord, if you, in your own proof,
Have vanquish'd the resistance of her youth,
And made defeat of her virginity,-- (Act 4, Scene 1)
The truth is, Claudio has no real proof, because there is none. He did not see what he thought he saw. His word is enough though, to ruin Hero's reputation. Hero faints and they tell everyone she is dead. Don John has ruined the wedding, and he and Don John have destroyed Hero's good name.