Reasons for using separate keys for signing and encryption:

1. Useful in organization were encryption key needs to be backed or kept in escrow in order to decrypt data once an employee/user of the organization is no longer available. Unlike the encryption key the signing key must never be used by anyone other then the employee/user and does not and should not need to be kept in escrow.
2. Allows having different expiration times for signing an encryption keys.
3. Given that the underlying mathematics is the same for encryption and signing, only in reverse, if an attacker can convince/trick a key holder to sign an unformatted encrypted message using the same key then the attacker gets the original.

Reasons for using separate keys for signing and encryption:

1. Useful in organization were encryption key needs to be backed or kept in escrow in order to decrypt data once an employee/user of the organization is no longer available. Unlike the encryption key the signing key must never be used by anyone other then the employee/user and does not and should not need to be kept in escrow.
2. Allows having different expiration times for signing an encryption keys.
3. Given that the underlying mathematics is the same for encryption and signing, only in reverse, if an attacker can convince/trick a key holder to sign an unformatted encrypted message using the same key then the attacker gets the original.

References

1. https://www.entrust.com/what-is-pki/

2. https://www.gnupg.org/gph/en/manual/c235.html

3. http://www.di-mgt.com.au/rsa_alg.html