If an user has his preference settings not to notify them on their own changes, and they share an issue with themselves, JIRA does not send any emails.

The share button should be independent of this setting.

Workaround:
You should be able to share an issue with your own user if you set JIRA to notify your own changes:

1. Click on your username in the top right corner.
2. Click on Profile.
3. Click on the edit button of the Preferences section.
4. Set My Changes to Notify me and click on update.