One is allowed to carry on Yom tov because they are allowed to cook... and carriying comes under the same category.. as it is related to preparing food... however why is one not allowed to create or distinguish a fire on chag if that is directly related to preparing food? (i.e. turn the oven on and off)

All Melachot that could have been done before Yom Tov and will not affect the quality of the food, even if they are related to the preparation of food, can't be done on the Chag. Similarly, only Melachot which are essential for the preparation are permissible. Fire can be lit from before the Chag and will not affect the quality of preparation, therefore can't be lit on Yom Tov. One can remove the pot from the fire without the need to extinguish the fire, yet, the food will be perfectly done, here again the Melacha is prohibited since it is not needed for preparation. (Shulchan Aruch OC 495, 1; 502,1)