I am here to provide years worth of research on how match ABSOLUTELY, WITHOUT A DOUBT pegs Firey (or wants to) as I have devoted 14 years of my life to this.
Notice how match and Firey were two of the first characters invented by Michael and Cary that are relevant to this day? They have a deep, thick bond. They are also designed as partners, match being a matchstick (lights fire wink wink) and Firey being the fire. This is supported by Firey Jr.’s existence. Could Firey junior be the offspring of match and Firey come sentient? Match and Firey are also known to be portrayed as partners. Quo the first episode, part 2. You can see match inviting Firey to her team, why not any of the other competitors? Along with this, Firey acknowledges this by referring to match’s decision to be a “good choice” and I could go on and on. During the naming of these teams, match on a megaphone stated the team name should be “Smoking Hot Firey Bod” and that is a clear factor that Match is IN LOVE or IN A CLOSE RELATIONSHIP with Firey.
In episode 16 of BFDI, during the points being considered, match says “Hi Firey!” In a tone that could be considered as some sort of flirt.
Notice how fires go on top of matches? This is also prime evidence that match is responsible for pegging Firey rather than any other action. This specific biological information is a key factor. Although, this does means that match gave birth by being inside a fire rather than a fire being inside her.