I'm going to venture to guess that your inspector is conflating a service with your feeder. A service is the connection from the house to the utility supply. Normally there is no over-current protection (fuse or breaker) at the source end of service conductors -- the utility assumes that the service conductors are safe from physical damage and it's adequate to protect against overcurrent by having the conductor size matched to the size of your main circuit breaker.
A feeder is different. You're building a feeder. Feeders are basically just a branch circuit that feeds other sub-branch circuits (via a subpanel). As you know, feeders do have overcurrent protection at the source end of the circuit, and in fact there's no requirement for a main breaker at all at your detached garage. A disconnect, yes, but no main breaker or fuse is necessary. As with any branch circuit, a person must size the circuit by doing a load calculation, then use conductors and other equipment that have ampacity sufficient for the use.
I think you might be able to reset and guide the inspector's view by bringing written calculations. Call it the "Detached Garage Feeder Calculations Sheet."
First, a load calculation. (See online calculator at Ask the Electrician, as helpfully pointed out in a semi-related answer by manassehkatz there) The process for this defined in article 220 of the NEC. Include items like general lighting and receptacles, any special equipment like an air compressor or welder, etc. Maybe even pad it out by including allowance for equipment you don't have any may never get -- a vehicle lift or an EVSE charger, for example. At the end of the load calculation section, highlight the fact that the minimum subpanel and feeder ampacity are X amps.
Second, show feeder conductor sizing calculations. This is really just as simple as "minimum required conductor ampacity -> chosen conductors are 2-2-2-4 aluminum -> all terminals are rated 75 C or greater -> OK, 2-2-2-4 is adequate and protecting it with a 90 amp breaker is appropriate."
Third, include some conduit sizing calcs for the mast and weather head (SER can't be buried!).
Finally, some commentary to wrap up your calculations. Something like the following:
- feeder's minimum ampacity is X amps; I choose to oversize and provision for 90 amps instead.
- will use 90 amp breaker model Y in main panel
- will attach 2-2-2-4 conductors to main panel
- will use conduit size Z
- will position disconnect model A with ampacity B amps on the exterior of the garage
- will use more 2-2-2-4 from outdoor disconnect to indoor subpanel
- will use subpanel model C, which could be lug-only or main-breaker style, with ampacity D amps because that's what's available and satisfies the calculated minimum of X amps.
And.. hopefully, when presented that way, the inspector will say to himself "ahh yes, this is right. What was I thinking?? Oh, I was thinking about a service.."
