Why did the Laki eruption of 1783 produce so much fluorine?
First things first about Laki: it's in Iceland, which means its source is a combination of an ocean ridge and a mantle plume. The plume contribution means that the source composition is relatively undegassed (unlike the source for most mid-ocean-ridge basalts (MORBs)!) and very basic, so contains relatively high concentrations of sulphur and other volatiles.

Secondly, it was actually a pretty high-volume eruption: per Gudmundsson (2011) it has been estimated that it produced 14 km3 of lava - compare with the estimated average global rate of magma emplacement and volcanic output of 26-34km3 per year.

The eruption style during the Laki eruption - not dissimilar to other Icelandic eruptions - is believed to have promoted volatile emissions during the eruption, including liberating up to 50% of F originally dissolved in the melt:


  The high degree of degassing at the vents is attributed to development of a separated two-phase flow in the upper magma conduit, and implies that high-discharge basaltic eruptions such as Laki are able to loft huge quantities of gas to altitudes where the resulting aerosols can reside for months or even 1–2 years.


Thus the significant fluorine release at Laki seems to have been due to a large-volume eruption degassing halogens extremely efficiently, with a relatively high initial fluorine concentration in the melt (~400ppm).