You might try giving him an example based in the real world. Choose one:
1) Go to a store that let's him get right inside and finish his business.
2) Go to a store that requires him to stop and listen to the sales guy standing in front of the store, telling him how awesome the store is that he's about to enter before being allowed to enter.
If he feels that a splash page is necessary for customer growth, suggest that he provide an intro on the front page in a prominent spot which people can turn their attention to if needed. This would be similar to walking into a store and seeing the greeter - you can stop and chat with them, or you can walk past without even making eye contact if you are already familiar with the place.
While the web is different than real life, it turns out that humans still operate on the same basic level. Forcing a person who is task oriented to go through the experience a meandering person might enjoy is simply going to irritate, and ultimately turn potential leads away.
Try to strive for a design that acts as a good entry point for everyone.