Follow these steps and you'll be fine:
- Make a list of 10 websites - half of them with splash screens;
- Sit with your client in front of a computer;
- Ask your client to visit the "About us" page of each site.
- Make sure your client visits all 10 pages.
Then explain to your client that
- users visit much more than 10 pages in a single session.
- users are impatent
- bounce rates are up because of splash pages.