Sends email to me but no to the person

Though the plugin successfully sends millions of emails every day, there are a host of issues that can stop or delay emails on both the sending and receiving ends. It depends entirely on your local Server & WordPress configuration. You will need to investigate this issue for your particular local configuration.

See Contact Form 7 Email Issues. There is a link at the bottom of the page to a comprehensive and detailed article which covers many issues. Most people that work through this information appear to be able to resolve their email sending & receiving issues.