To boast is to tell others that there is something special about you which means they should respect you more. To show favoritism is to say nice things of someone even though you do not really mean it, with the hope that they will think fondly of you. It seems as if this boasting and favoritism were done in order to gain financially. Maybe the church to which Jude was writing was relatively rich and these false teachers were seeking to enrich themselves. They are thus in the business of religion but have no real piety toward God, taking advantage of his people for profit.
16 These are grumblers, malcontents, following their own sinful desires; they are loud-mouthed boasters, showing favoritism to gain advantage.