It is for told that evil will clash with the good in this world and only those strong enough to resist the temptation to do evil will get and keep their wings.
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The story goes that long ago angels and demons were able to live in peace without being titled as such. There were a few(the demons) who got it in their head that power was the most important thing, those who all believed in the cause joined together and brought hell down onto the heavens and were then sentenced to live out their lives without their wings and were titled as 'Garms' or 'Demons'.
Over time, the demons lost the ability to even gain wings while the angels had to complete a special task to gain their wings, if they failed they would then take another one a year later. If an angel was to commit a crime they would to lose their wings with a stub as a reminder that they were once able to soar the skies.