I have been meaning to write this for the longest. Science and magic correlate in many ways. Often, people think magic is what they see in movies. However, real-life magic is energy-based and still follows certain laws within the sciences. It cannot defy physics, thermodynamics, nor genetics. Here are the general scientific explanations as to why certain things such as physical transformation, becoming a mythical creature, telepathy, telekinesis, etc. are impossible.
Newton's three laws of motion apply to how one's energy influences the outcome. The first law is the law of inertia. Energy will continue to flow at constant motion until extra force is applied. In terms of magic, energy must be put into one's spells or rituals to achieve the desired outcome. The second law is the net force equates to the mass times acceleration. In terms of magic, the amount of energy and its flow plays an important role in spell casting. Some spells and rituals require more energy than others. If the amount of energy, or the speed of its flow changes, the net force applied will change as well. The third law states what is put in equates to what is put out. The amount of energy the caster puts out equates to what will be put into the caster. Therefore, caution must be taken when casting certain spells as the type of energy puts out may return to the caster. This concept is quite similar to the Law of Attraction. If one puts out negativity, negativity returns to them, and if positivity is put out, positivity will return to them. There is a theory called the observer effect. The act of observing will influence the target that is being observed. Think about intentions and willpower. Once a target person is selected, the caster uses their energy plus intentions/willpower to affect the person and even their way of life.
Magic is asserting one's energy to influence the outcome. How does our energy allow our intentions to manifest? Through the laws of thermodynamics. Energy cannot be created nor destroyed, only transferred or transformed. Our energy is constantly moving, transferring into others or our surroundings, whether intentionally or not. For those who do not protect their energy through grounding and shielding, they tend to feel very drain because their energy is not being used to their desire (similar to wasting energy). Their energy is being transformed into something else. What do I mean by transform? Imagine you are out camping. You gathered enough wood to start a fire. When you rub two branches together, using friction to start that fire, you are using your energy, which is being transferred to the friction and transforming that energy into it, giving rise to sparks, which give rise to fire. You then place a pot of water over that fire. The energy in the fire is being transferred and then transformed so that the water can begin to boil. Another example is riding a bike. The energy that the person puts in to move the petals is being transformed into a different energy, which then transfers into the wheels of the bike, allowing the bike to move. Similar to these examples, when we cast a spell, our energy is being transferred, then transform to our spells and rituals, allowing it to manifest.
The purpose of this portion is to explain why transforming one's physical appearance into a supernatural creature or anything else is impossible. During DNA replication, the enzyme, helicase breaks down the hydrogen bonds, allowing the helix to unwind. Primers, nucleotides (A, G, T, C), polymerases, and other enzymes aid the replication process. The A nucleotide is paired with T, G paired with C. When there is an error in one or more nucleotides (ex: A pairs to C error), the system can fix this through various proofreading techniques. It is rare for an error to remain unresolved. The chances of a mutation occurring through this is usually 10^-6 percent ( 0.000001%). In terms of genetic disorders, when these mutations occur, it affects the transcription and translation process. DNA converts to RNA in transcription, RNA converts to proteins in translation. There are 64 different codons in proteins: AUG will always be the start codon and UAA, UAG, and UGA for stop codons. If the mutation changes an amino acid into one of these stop codons or a completely different one, it can be the cause of a life-threatening genetic disorder or a genetic illness that can affect the person's way of functioning.
Keeping in mind the rules of physics and thermodynamics, telepathy, telekinesis, teleportation, flying, and any other physics/thermodynamics-defying claims are impossible. Keeping in mind the basic understanding of genetics, transforming into a vampire, werewolf, mermaid, and any other mythical creature, deity, animal, etc. is also impossible. Magic is using one's own energy to influence the outcomes they desire. It is subtle changes that take time to manifest. I understand that science has yet to prove everything, however, that does not mean magic and science do not correlate at all. Science and magic still go hand and hand. Magic is nothing like the movies or shows we see, but it is very effective in many subtle ways.
And of course, another shout-out for Ashen-Heart's phenomenal article, "Magick: how does it work? Physics has some answers!": https://www.spellsofmagic.com/coven_ritual.html?ritual=4185&coven=245