Maybe "believe" is not the right word. People "believe" in the Easter Bunny or in Santa Clause. But on the issue of global warming, aka climate change, a body understands or does not understand what climatologists are trying to say.
An irony is that the science appears to scandalize some people only on the surface. Deeper down it's the social political and economic implications, and that the message comes from "those people over there, who are not like us".
Climatologists study weather long term. Most of what we know about climate has come from them. People point out that climates have always changed. The better part of the understanding of that comes from climatologists.
For decades they detected some things that are distinctive about the current regime. They were working away quietly until a relatively few years ago. Then the matter got very public. To their general chagrin. Remember that '70s song, "What Have They Done To My Song, Ma?" by Melanie?
Nobody else knows climate like climatologists, and these days, after a lot of research and a lot of thinking, they are virtually unanimous in the opinion that the climate is warming dramatically and that our activities are a critical factor. It's serious, they say.
A critical factor, maybe a deciding factor. Not the only factor. They tell us that for sure the climate has always fluctuated for many internal systemic reasons, thru the vagaries of solar output, and purely by chance. But these days they add, there also is the growing and powerful influence of our own additions to the atmosphere piling on too.
Climatologists these days actually do know quite a lot about climates of the past. Methods and technology, and the sheer number of minds that have been working on the question for a very long time, have produced a remarkably clear and detailed picture of the past and a very good idea of how the atmosphere works.
In simple terms the atmosphere is something like a chain saw. If you add too much oil, or run it too rich or too lean, it doesn't work well. In fact, it can even stop working altogether.
Same with the atmosphere. If you suddenly release into the atmosphere all of those compounds and elements that had been stored in the earth for hundreds of millions or billions of years, the atmosphere simply can't handle it. All at once is the 200 hundred years since the start of the industrial age. The hundreds of millions and billions of years is the period since the creation of the fossil fuel deposits. Our atmosphere and all of life evolved with a dependency on a much, much slower rate of release of these compounds and elements.
Just as in the days of the debate about the effects of smoking, industries with a lot to loose have been sowing as much doubt and confusion as they possibly can. It doesn't take much. And really, now most of the criticism isn't about the science, it's about the "professors", the "liberals", the "government". And that's the way industry would like it, so people won't stop to consider the science. They'll focus on mistrust instead.
In any case, climatologists are the people who can see the big picture. They are our instruments. The old pilots' saying is that "when you start doubting your instruments, then friend you are in trouble".
The current run of weird weather, like many other recent patterns and incidents, is not attributed directly to global warming. It's about air masses out in the Pacific.
But the verifiable, rapid and worldwide rise in temps, among other things it does, interacts with natural occurrences. It can exaggerate them, make them more frequent, and just generally throw a wrench into the works of the only atmosphere we have.