Why did Joseph wish to divorce Mary?

Joseph had four options. Stoning, divorce with public humiliation, writing a certificate of divorce with a couple witnesses, or continue with the marriage contract.

Capital punishment was not allowed by the Romans just for the violation of a Jewish crime and marriage after suspicion of adultery would have meant Joseph accepting the dishonor and shame of a "defiled wife"--which eventually he did do.

Joseph originally chose the less severe of the two forms of divorce out of compassion for Mary, even though it could have meant forfeiting the financial remuneration he could have received.