From LinkedIn help (italics are mine):
By default, your 1st-degree connections can see your list of connections. This lets them browse your network and find mutual friends and colleagues. No matter which setting you select, your 1st-degree connections will always be able to see shared connections.
Your connection may choose to hide connections they don't want to share. In this case, there won't be a See connections option on the member's profile.
It's a LinkedIn feature. Your connections can choose whether they wish to reveal NON-SHARED connections or not. Within Settings > Who can see your connections, they can select one of two options in the dropdown:
- You (so no one can see the non-shared connections)
- Your connections
When you asked your connection to make the change, he changed the preference from the 1st option to the 2nd.
Note: You cannot hide shared connections from your 1st degree connections.