I've seen a lot of artists and writers interpret different breathing styles in swap aus or any aus where the Demons are slayers. However realistically speaking which actual breathing styles would they use that aren't made up ones? First let's break down breathing styles-
WHAT IS A BREATHING STYLE?
According to the kny Wikipedia page-
Breathing Styles are swordsmanship styles that makes use of an esoteric breathing technique known as Total Concentration Breathing practiced and taught by members of the Demon Slayer Corps and are used in combat by (later passed on as traditional dances post-time skip).
All known Breathing Styles currently taught within the Demon Slayer Corps are derived from , the first one ever created. The majority of known Breathing Styles mimic a certain element of nature (i.e. flame, water and wind) and replicates it with the user's movements, techniques and abilities. The weapon attacks of Demon Slayers who use Breathing Styles are also longer ranged, possibly due to shockwaves or air pressure generated from their weapon itself when swinging and striking.
Order OF BREATHING STYLES AND THEIR CREATION
Again according to the sources, Sun Breathing was the first ever technique developed by Yoriichi Tsugnakuni and from it came the first six breathing styles used by slayers in the show minus Moon Breathing specifically only used by Kokushibo since developing it and transforming into a demon-
Stone Breathing
Moon Breathing
Thunder Breathing
Flame Breathing
Water Breathing
Wind Breathing.
From five of these breathing techniques, the various other breathing styles were created from them.
Flower Breathing used by Kanae Kocho and later used by Kanao Tsuyuri was derived from Water Breathing as was Serpent Breathing developed by Iguro Obanai.
Insect Breathing was formed from Flower Breathing by Shinobu Kocho.
Beast Breathing self taught by Inosuke Hashibara and Mist Breathing used by Muichiro Tokito are derived from Wind Breathing.
Love Breathing created by Mitsuri Kanroji developed from Flame Breathing.
Sound Breathing created by Tengen Uzui was developed from Thunder Breathing.
The breathing techniques used in the show's current time were all passed down either by teachers like Urokodaki or Jigoro, through families like the Rengokus, developed by others from the original styles, or in the cases of Kokushibo and Tanjiro, was only ever used for themselves or passed down by other various means such as the Hinokami Kagura dance developed presumably by Sumiyoshi Kamado, Tanjiro's ancestor.
BASIC IDEAS ON THEIR BREATHING FORMS AND HOW THEY WORK
I won't be deep diving into every form every breathing styles has and I'll be excluding Moon and Sun Breathing for obvious reasons. Again all info comes from an info website Screen Rant-
Flower Breathing: Flower Breathing is said to be derived from Water Breathing and shares certain traits in common with it. While the numbering of the forms for this style indicates there should be at least seven, only five are used in the series, and the final form can cause blindness for the user. Kanao doesn't get a lot of focus, and as a result, Flower Breathing comes across as underpowered.
Insect Breathing: Because Shinobu isn't physically capable of decapitating most demons due to her size, this style relies heavily on poisons, mostly created from the wisteria that demons hate. Insect Breathing only has four known forms as well, limiting the options Shinobu has during battle. Shinobu's track record in battle with it is mixed, to say the least, so it seems like Insect Breathing has drawbacks when fighting anyone who's aware of its poisons.

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