Sharks are mindless killing machines that must constantly eat
Pretty sad how pop culture depicts such amazing misunderstood creatures (though slowly but surely the popular opinion is changing). For starters, most sharks don't even feed every day, as being "cold-blooded" doesn't require as much fuel. Even for large active sharks with elevated body temperatures, great whites can go without food for about one and a half months if need be! Sharks, being highly capable predators, are definitely smarter than we give them credit for (even goldfish aren't that dumb, have a longer memory than a few measly seconds). They have interspecial social hierachies, preferred types of prey (except at least a few species), play, mating rituals, migration patterns, ways to decipher if an unknown thing is a predator or prey (which is why you shouldn't splash and dart away like crazy if pursued by a large capable shark) and other ingrained features that they only seem like "killing machines" the less you know about them. If anything, humans are more deserving of that title but I'll plunge into that in a bit.
The only part of a shark to fossilize is its teeth
While shark teeth make up by far the most common shark fossils, other hard parts are also known to fossilize at times. Their disc-like vertebrae made of caalcified cartilage are found at times, as well as their skin cartilage, dermal denticles (small tooth-like protective structures), rostral nodes (cartilage near the snout), fin spines (for species with those), and coprolites (fancy term for fossil poo) are among accesory shark fossils. In rare, favorable fossil forming conditions whole sharks may be found fossilized!
All Sharks are dangerous and actively hunt humans
While some species (bull, tiger, great white) are large and known to sometimes attack humans while unprovoked, the majority of shark species don't care about us. They have survived for millions of years without human flesh and much prefer fish or other aquatic prey than some odd looking ocean guests.
All sharks can grow large and have big sharp teeth
As one of the most ancient group of vertebrates still around today, they have had plenty of time to diversify and modern sharks reflect this. Some have grinding plate-like teeth (i.e. port jackson shark), some lie motionless on the ocean bottom and ambush nearby prey with suction, some have practically no teeth and only swallow microscopic prey, and some even have "saws" on their snouts! Nearly 500 shark species live today (in 8 orders and 34 families) and many definitely do not reflect the typical shark profile.
Sharks are more dangerous to us than we are to them
Tens of millions of sharks die each year from commercial fishing or finning (an extremely wasteful old practice of cutting off a live shark's fins, dumping the body to die just to alter the consistency of a soup) while only a handful of sharks kill people each year, and over half of attacks yearly are linked to board sports (majority of shark attacks on humans do not result in death). This fact has thankfully been spreading like wildfire lately but it is still a vital fact.
Sharks are actually dinosaurs
Nope sharks are fish, even if they have no "bones" (unlike typical fish). This misconception likely arose due to the fact modern-esque sharks were around at the time of the dinosaurs, but dinosaurs are land-dwelling tetrapods, no ocean dwelling fish.
Rays are just flattened sharks
Rays/stingrays are definitely extremely closely related to sharks, both are cartilaginous fish and share many of the same general characteristics, but enough differences still exist to put them in different groups. But I have heard scientists state rays are practically flattened, specialized sharks, similar to how snakes can almost be considered legless lizards (both share a not too distant common ancestor, but still separated from each other millions of years ago)
Since Sharks are fish, they can be fished heavily with little to no risk of extinction as they rebound quickly
In general sharks are much less resilient than bony fishes, as they reach sexual maturity later in life and have less offspring. This "quality over quantity" strategy has worked wonders for them in the natural world, securing their place among the very top predators in the ocean, but makes them much more vulnerable to extinction in unfavorable conditions and/or when overfished. Many shark species' stocks are continually declining worldwide due to unsustainable fishing practices.
Megalodon was so massive it would've had a difficult time hunting down prey so it only scavenged prey
While I have no doubt Megalodon sharks were opportunistic predators and certainly scaveneged its food when it could, this was likely not enough to sustain the species. This notion has been abandoned as fossil bite marks on whale bones show they took down whales at high speeds, as extensive damages show. Lamniform sharks are known to be very active predators and in order to reach 50 or 60 feet in length (let alone sustain a whole species of sharks that reached this length) it would have to take down a lot of whales and other large prey regularly.
Sharks are just another fish in the sea, their demise will have no consequences
Much like believing sharks are mindless killers, this could hardly be farther from the truth. Marine ecosystems are an intricate interconnected system with every link serving an important purpose to sustain the system. With the sudden elimination of one link, an imbalance is created and the whole ecosystenm is more prone to collapse.
Bull Sharks have the highest known testosterone levels in any animal
This one seems to be thrown around a lot, even among scientific communities, but is misleading. This statement is based on one obscure measurement of a bull shark having 358 ng/ml (probably the highest measurement known) of testosterone, but the other male bull shark only had 2.7 ng/ml. Male elephants have around 2 ng/ml but when in a rage, it may increase to 60+ ng/ml. A subsequent study of captive male bull sharks over three years (just after the normal breeding season) only found levels of 10 to 20 ngl/ml (to be continued)
Higher levels have been found in male bull sharks out in the ocean before breeding season (185 ng/ml on average) but even the diminutive cousin of the hammerhead sharks- bonnethead sharks- have been recorded of having 303 ng/ml.
I'm not saying it's not possible some male bull sharks have super high testosterone levels, but it is definitely a stretch to stereotype the species as a whole for being "constantly 'roided out".
Sharks cannot get cancer
While sharks & other elasmobranchs (cartilaginous fish) are much less susceptible to forming cancer, there are several cases of sharks getting cancer; and even cancer on their cartilage. It should perhaps not be too surprising entrepreneurs take advantage of the myth shark cartilage is the key to a healthy, fulfilling life when in reality there is zero evidence ingesting shark cartilage provides any benefit, and even if it did, is it worth slaughtering millions of perfectly fine sharks? Our ecosystems need as many sharks as possible.
Sources:
https://phys.org/news/2017-01-global-shark-average.html\
http://www.fossilguy.com/gallery/vert/fish-shark/remnant.htm
https://blogs.scientificamerican.com/science-sushi/mythbusting-101-bulking-up-with-bull-shark-testosterone/
https://blogs.scientificamerican.com/science-sushi/mythbusting-101-sharks-will-cure-cancer/