Because they mostly have no clue that measles is a potentially fatal illness, with potential severe lifelong complications including some which require 24/7/365 full nursing care.
They think of it as a mild rash with mild flu-y symptoms for a week or two.
They also have no idea it is so very contagious.
So though the measles vaccine has an amazing safety & efficacy record, whether singly or as part of the combined MMR, with endless research turfing up no link to autism whatsoever, and carrying only a negligible risk of vaccine injury (none as severe as the complications of measles), those who reject it do so not only out of totally false beliefs about the vaccine, but also out of fully wild misconceptions about the risk of measles.
Though now the anti-vaxx movement has become such a big thing for a while, they're all egging each other on with the help of ideological pundits. This combines to create a group highly distrustful of public health organisations and all medical advice on the matter, who are much more resistant to accepting correct information than their vaccine-shy counterparts ever were in the past. It also seems to be true that scary conspiracy theories are comforting to them in a world where serious infections can just catch a person, where autism isn't something one can simply opt out of - they want simple answers, and everything which debunks that simple wilful ignorance is a threat to their sense of security.
Years ago, my parents set out on a long journey from their home city to a rural location in another country.
Approximately five minutes after setting out, a car went flying past them. It was a bright red sports model that was very eyecatching.
Not long after, they arrived at a toll bridge, right behind the same red car. They noted the number plate.
Past the toll, the red car sped off again, quickly accelerating well past the speed limit.
Over the next few hours, this repeated at a major junction. When they eventually arrived at the ferry again just behind the red car, my father flashed his headlights.
Disembarking, they got another flash from my father, and sped off.
Several hundreds of miles later my parents arrived at their destination, parked up, and got out to stretch, when pulling in beside them was a curiously familiar red car.
Not wishing to make assumptions, my mother casually checked the plates, then saluted the driver and inquired about their journey to the event they had all arrived for.
Nope, they'd made no detours or stops, they'd taken the same route.
My mother has a way in these situations of wording things just so, that totally makes the person she's talking to feel like an absolute worm without ever getting the escape of thinking my mother was being anything other than lovely and charming to them.
Red car was spotted driving most sedately in the local town the following afternoon.