Your agent is not your lawyer

He just want his commission.

As a landlord, it is in your interest that both of them sign the lease, so that you can go after either one of them for FULL rent.

As unmarried tenants, it is in their interest to have only one person as lease holder, and the other being occupant/guest, so that they can break up anytime without being tied to the lease.

What should you do as a landlord? You TAKE CARE OF YOUR OWN INTEREST! Stop being friends to your tenants.

You tell them both of them sign NOW, and if one wants to move out, you promise you'll release one of them off the lease and sign a new lease with the one leaving behind. But that's oral promise, you still get their signatures NOW and hold BOTH of them responsible.

And when you review income/credit score, make sure evaluate them separately to make sure any one of them qualifies with full rent.  Don't assume they will always split 1/2.