Date: 201707
Local time of day: 1801-2400
Location: LAX.Airport, CA
Flight conditions: Mixed
Weather elements / visibility: 4
Light: Dusk
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class B LAX
ATC / advisory: TRACON SCT
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown; Confusion
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Contributing factors: Airspace Structure; Procedure; Company Policy
Primary problem: Procedure

Narrative: On the STAR on a 'Descend Via' clearance; talking to Approach; we were cleared for the ILS Approach while passing through approximately 16;000 feet or so (maybe higher). Weather at was 300 feet overcast; with tops around 1;000 feet but clear above. I planned to fly a CAT-III on the HUD; in case weather got worse. At around 8;000 feet; Approach told us of traffic; and instructed us to 'maintain visual separation.' I asked the First Officer to decline it; which he transmitted to the Controller. The Controller remarked in a somewhat surprised tone; 'Why?' I keyed the microphone and said something like; 'Because we'll be in the clouds.' I was not as clear as I wanted to be in my transmission; because we were busy on the ILS with all the step-down fixes; but I was referring to the fact that we were cleared for an ILS Approach; and I'd be flying a CAT-III; and I didn't need more 'task loading' to make things easier for ATC.The Controller switched us to a different frequency; and the new Controller pointed out additional traffic and told us; again; to 'Maintain visual separation.' I keyed the microphone and said that we were not going to comply with that instruction. The Controller then issued speed adjustments to other aircraft.I am not understanding how a 'Descend Via' or 'Cleared ILS' instruction can be given; with a 'Maintain visual separation' instruction. In my opinion; ATC cannot have it both ways. An IFR instruction which requires us to maintain an exact lateral path; vertical path; altitude; and airspeed; while maintaining Visual Separation. I feel it should be one or the other; but not both. Additionally we are so busy with the very-complex STAR and ILS (which; in my opinion was designed to make it easy for ATC; but not us); and combined with low weather at the airport; that the last thing I want to be doing is guessing if we'll be clear of traffic that is joining final next to us! The truth is that a lot of 'maintain visual separation' compliance is guesswork by us Pilots. We try to comply to keep things going well; but especially at night and hazy conditions; it's almost impossible to judge closure rates and altitudes. I'm not there to do ATC's job. If ATC expects us to fly these complex STARs and ILS approaches; they can't expect us to conduct spacing as well. Their primary job is separation; and they need to be doing just that; not mere sequencing of aircraft toward the runways; leaving separation to us.




Synopsis: B737-800 Captain reported refusing ATC's instruction maintain visual separation from parallel runway traffic.