Claudio refused to marry Hero because he thought that she was cheating on him.

Claudio was tricked, by Don John, into thinking that Hero was cheating on him with another man.  He did not actually see anything.  What he saw was Hero’s maid, Margaret, at a window, and he thought that it was something else.  Don John arranged the whole thing to discredit Hero.  They say some people are in love with love.  Don John is in love with hate.

In Act 2, Scene 2, Don John and Borachio designed the insult to Hero’s honor.  They would make it look like Hero was with another man, when really it wasn’t Hero at all—it was just her window.

BORACHIO

I can, at any unseasonable instant of the night,appoint her to look out at her lady's chamber window.

DON JOHN

What life is in that, to be the death of this marriage? (Act 2, Scene 2)

Then Don John just had to make sure that Claudio went to the window and saw “Hero” doing the dirty deed.  He would then doubt his girl.   Don John tells Claudio that Hero has been “disloyal.”

DON JOHN

I came hither to tell you; and, circumstancesshortened, for she has been too long a talking of,the lady is disloyal.

CLAUDIO

Who, Hero? (Act 3, Scene 2)

Claudio, being the rapscallion that he is, decides not to confront Hero until her wedding day, where he can disgrace her before everyone they know, and tell her then that he isn't going to marry her!  He calls her a “wanton” and while everyone is completely confused, he hurls insults at her.

Out on thee! Seeming! I will write against it:You seem to me as Dian in her orb,As chaste as is the bud ere it be blown;But you are more intemperate in your bloodThan Venus, or those pamper'd animals

That rage in savage sensuality. (Act 4, Scene 1)

This is, in some ways, one of the most tragic scenes in all of Shakespeare.  Poor Hero has done nothing wrong, and dies a symbolic death.  Her reputation ruined, Claudio believes the worst of her without reason.  He was deceived, and she has no recourse.  The solution that they come up with is to tell everyone she is dead, but in some ways, she is.  Claudio refused to marry her, but no one else would either.  Everyone will believe his accusations.

Claudio's behavior after this is just as bad.  He agrees to marry a "substitute" for Hero, as if women were all interchangeable.  The substitute turns out to be Hero, but why would she want to marry this clown anyway?  The truth is, she has little choice.  Even after the truth comes out, the smear he has done to her will follow her ever after.  It may be Don John's work, but it is Claudio's fault for not believing in her goodness.  He said he loved her.  He should have given her then benefit of...