The ideal existence for a parasite isn’t always symbiosis. The maths that relate transmission & pathology have been worked out but there are many cases where a parasite causes it’s host to commit suicide. The fluke ‘Dicrocoelium dendriticum’ causes the ants it infects to climb blades of grass at the end of the day instead of seeking the shelter of the colony thereby instigating it’s own predation & death (there are many other examples). In this way, the fluke ensures it’s transmission to a new host and it’s survival.

If you, as a parasite, are not too numerous, then killing your host may be good strategy.