Because plasma is sometimes considered as the fourth state of matter.
Einstein's famous equation \(E=mc^2\) tells us that matter is equivalent to energy, and so does the other way around, in this case, fire is rising air with oxidizing chemicals in them, since it is made out of gas molecules (i.e. matter), it is an alternative form of energy.
It is easy to misintepret that fire is a kind of plasma because of its similarities and uniqueness, but in reality, although fire does ionize atoms, due to the lack of temperature and energy intensity unlike welding arcs and lightnings, most of the atoms are just in the form of heated gas rather than a plasma.
Conclusion: It is both matter, energy, and partial plasma but mostly gaseous.
Thank you! You are a genius! You should be a scientist (or are you one already?). But I have to say... I skipped most of your explanation and looked at your conclusion...
And are you related to Albert Einstein?
I studied particle physics for three years, I might aswell be classified as a "scientist" if you want so.
(How dare you skip over my explanation XD)
Yeah, he’s related to Einstein – the same way a turkey is related to Einstein.