I'm sorry, but that's really what creationism is all about: They think science is wrong about the past. They say that scientific proofs are invalid and that science only makes assumptions that are not backed up by evidence.
Instead they take the Bible as fact, because it is the word of God. They back up that believe by saying the people who wrote the Bible were inspired by God to do so. And as a result the Bible can't be wrong.
In the Nye vs Ham discussion you may have noticed how Ham insists there's a difference between "observational science" and "historic science". The former basically is the science about the present, which our technology etc. is based on and Creationists don't really argue with it. The latter is the science about the past, which creationists believe is wrong due to lack of evidence and too many assumptions. Ham brought the example of ~40'000 years old wood embedded in ~40'000'000 years old basalt to prove that scientific dating methods are incorrect. While doing so he explicitly ignores the fact that both methods come up with results that are way beyond what he claims to be the age of the world.
It all boils down to creationists saying that scientific methods for research about the past are all wrong. At the same time all they have to back up their own claims is "there's a book about it and it was written by people who acted by god's command" or something like that. To avoid having to mess with scientific terms, they use their own ones. For example the blurry term "kind" instead of a more specific term like "species". Apparently a "kind" already has all genes required to form a number of species. All it supposedly takes is genes turning themselves on or off - no scary non-religious stuff like "evolution" required.
Creationists pick away at individual weaknesses of modern science, which may or may not be stabilized in the future. They purposefully attack these points, seeding doubts among less-educated people, all while ignoring many other facts that put the entire scientific construction of knowledge about the world on a very very solid basis. And they only do this to prove their very fragile calculation of the age of earth correct. That calculation is based on a single source that is taken for granted instead of being backed up by any kind of actual testable facts.
Science bases all its work on the principle that a theory must come with a way to prove it wrong. And a scientific theory isn't just guesswork, but based on observed facts. You can easily prove it wrong by observing a different fact that doesn't fit in. Scientists will be excited if you can prove them wrong on very basic things. That's what drives science. Creationists are no scientists (at least not for the topic of what happened in the past) because they say "there's a book and you can't prove it wrong." That's the difference between science and religion.
You may be right on some of that but you are pretty far off on a lot of it.
The first paragraph is only true for the vocal crazy people that understand there is no such thing as bad publicity when seeking to be famous. However those people actually laboring in the scientific field don't like to be associated with crazy people because it is very difficult to be taken seriously as a scientist if some broad label grouping you with infamous loons is applied to you.
Basically the label of creationist literally covers anybody who holds a different view of the origin of the species then the excepted evolutionary model or a direct variation there-of. Regardless of how much or how little scientific evidence there is behind there theories.
So your notion that all creationists are crazies is a bit bigoted. However those want to be in public eye for it most likely are.
Carbon 14 dating is rubbish in the terms of a definitive benchmark because there are multiple anomalies that can influence the amount of carbon 14 that could be present in the specimen being dated. (carbon14 levels can very due to natural gas, volcanic activity, geothermal gasses, and other localized phenomena that can skew results.) However, as you vaguely alluded to, carbon 14 providing a dubious timeline does not evolution disprove.
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As to the prevalent young earth notion...
The Bible does not fix the age of the earth, contrary to the claims of Ken Ham and others. Historically, these claims come from the work of James Ussher, Bishop in the Church of Ireland, from 1625 to 1656. Archbishop Ussher took the genealogies of Genesis, assumed they were complete, and calculated all the years to arrive at a date for the first day of creation of the earth on Sunday, October 23, 4004 B.C. Of course, even assuming the method was valid, such an exact date is not possible from the genealogies of the Bible (Ussher assumed all the years the patriarchs lived were exactly 365.25 days long and that they all died the day before their next birthday). There are a number of other assumptions implicit in the calculation. The first, and foremost, assumption is that the genealogies of Genesis are complete, from father to son throughout the entire course of human existence. The second assumption is that the Genesis creation "days" were exactly 24-hours in length.
Most people who read English translations of the Bible assume that the English words have the same meaning as the original languages in which the Bible was written (Hebrew and Aramaic for the Old Testament, and Greek for the New Testament). In fact, the original biblical languages contained many fewer words than modern English, which means that the words in those languages had more different meanings. In the Genesis 1 creation account, each "day" ends as "evening and morning 'n' day,"5 where "n" is the day's number. Although many Christians claim this makes the days exactly 24-hours in length, the Hebrew word translated "day" in English actually has three literal translations; the daylight portion of a 24-hour day, a 24-hour day, and a long, unspecified period of time (as in "day of the dinosaurs").6 The Hebrew word translated "evening" also means "sunset," "night" or "ending of the day." The Hebrew word translated "morning" also means "sunrise," "coming of light," "beginning of the day," or "dawning," with possible metaphoric usage.7 Our English expression: "The dawning of an age" serves to illustrate this point. The intended meaning of the word should be determined from the context.
Which complicates the concept of a 7 day creation...
2 Peter 3:8
But do not overlook this one fact, beloved, that with the Lord one day is as a thousand years, and a thousand years as one day. So 7 days of creation or 7000yrs [shrugs] whoops made it a tad more complicated.
Ironically though if God exists and is a space traveling being as the bible implies this would make sense according to physics if he has the ability to travel faster then the speed of light.
Genesis 1:11-12
Then God said, "Let the earth sprout vegetation, plants yielding seed, and fruit trees bearing fruit after their kind, with seed in them, on the earth"; and it was so. And the earth brought forth vegetation, plants yielding seed after their kind, and trees bearing fruit, with seed in them, after their kind; and God saw that it was good.
'Let the earth sprout vegetation' sounds like cultivation and agriculture to me, not 'and poof there were green things' further sounds as if things took a tad bit of time.
In multiple places the bible says '...remember His covenant forever, The word which He commanded to a thousand generations... in most places a biblical generation is 40 years. Now my math is a little rusty perhaps but I am pretty sure that alone exceeds 6000 by some 34,000 years.
Basically I have to wonder if Ken Ham has ever read the bible and understood 1/10th of it.
There really isn't any evidence that proves evolution. There is correlating evidence that supports it, but correlation doesn't imply causality. The same data that 1 group identifies as indicating a progressive linear micro evolution can be interpreted as having a common designer. Though beyond that data to indicate that the creation spoke of in Genesis or any other variation of the story happening is almost nonexistent and there is almost an entire lack of evidence that would factually dispute evolution. Other biblical events certainly... Conversely there are certainly plenty of issues that plague the theory of evolution but you will never see an evolutionist happily embrace it as evidence to the contrary.
History is full of examples of science dragging it's feet when it comes to change. So the comment "Scientists will be excited if you can prove them wrong on very basic things" and its mirror in the debate is BS.
Rogue waves are a good example there. Not that you can expect Ken Ham to EVER change his tune, so by contrast though an extreme exaggeration IMO I wouldn't call what you said fundamentally incorrect.