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Lets get this straight. Solgaleo isnotbased off the sun. It isThe Beast thatdevoursthe Sun. And while it is weird to have something that literallyeatsthe sun be weak to it, it is just an alchemy lion … that looks like the sun.
It’s not “based off the sun” though, it is based on the metaphorical imagery representing the purification of gold in alchemy, and it is the sun’s emissary not the embodiment of the sun itself. Furthermore, the sun itself doesn’t work that way. The sun isn’t burning, there’s no fire in or on the sun. It is a nuclear fusion reaction, not a burning object. While it may be slightly counter-intuitive for Solgaleo to be weak to fire, it is in no way as strange as people keep making out.
That was a great explanation, thanks Bulbapedia.
Source
EDIT: adding these facts (credit to SYL and Consider7)
Even better it’s the purification of gold and gold is a metal
Google says when Solgaleo is using it’s power, it starts to glow like the sun.