Like mentioned before me Game Freak hasn't confirmed it so we can't say for sure however I do have some hypotheses
Weakness (Explanation)
Steel
I believe it's weakness to Steel could be associated with the fact that steel and iron can deflect many if not all forces that don't use physical pressure to hit it as Fire doesn't exactly damage steel but rather forces it's molecules to spread. With fairy magic often displayed as a light yet powerful force it seems logic to me that steel is able to deflect their magic and send it flying against them as steel is often the material of which holy weapons are made. Weapons that are created to fight higher forces such as magic. Excalibur is a nice example of this
Poison
Fairies are often benevolent creatures and they have been shown to be much stronger then their size portrays them to be. However they have also shown to be quite frail. Though they have the ability to help others, the ability to cure themselves or others is not permitted to them and with this the easiest way to kill a fairy is to intoxicate it as it will quickly die should help not be rendered soon
Resisted by (Explanation)
Fire
I believe that fire can't be stopped by fairy because fire is a primitive force. One that has existed much longer then fairies and is with this a mystic and powerful form of magic. Fire is also a type of magic that can't simply be stopped by a common spell as it can scorch the spell into oblivion. In order to hit bewitched fire a fairy must summon rain or water and with this attempt to quench the fire. The need to summon water can be associated with the simple fact that they are not capable of doing the job themselves
Poison
The fact that they can't heal themselves with their powers states that their magic does not match up with that of intoxication as they themselves can either cure themselves as well as another living being. They often do know how but just don't have the ability to.
Resistance to(Explanation)
Dark
Fairies are often thought to be only benevolent but there are many in their species name that are rather dirty, filthy, double-faced and or sinister and sly. With this they have wide knowledge about dark arts as well an know how to use it as well as stop it. Good Fairies and Dark Fairies and or Dark Forces have a blistering rivalry however as often as they fight each other, none tends to win causing the fight to often be set still as they plan to attack again
Bug
Bugs are known to be one of the frailest living creatures in a fairy tale ad with this often stand under the protection or under the power of a guardian fairy. With such loyalty to them it is normal that they are not in the state to damage them very much
Fighting
Fairies have also shown to be very wise creatures that fight only if it is the last resort. With this they can easily avoid a fight as long as they desire as their mental abilities are great. And as following attacks from aggressive beings(Humans) don't tend to damage fairies much and is with this also rare for they might be mostly little but the power they contain is stunning. Though it is never too much for a target to bare
I personally think that these things might be the reason behind it's resistances and weaknesses
