I believe the basis of the idea that losing some public sector jobs does not substantially hurt the economy is that the public sector consumes more than it produces. It's not a profit center.
For this reason governments cannot drive economies; governments produce nothing, and because of inherent inefficiencies the public-sector contribution to the economy is therefore never as large as the tax burden required to sustain it.
Are there valid reasons to have public-sector employees? Absolutely! However, the context of Laralus's post dealt specifically with the narrow question of economic policy, and why reducing the number of government jobs wasn't necessarily a bad idea for the economy.
There's no reason to get upset, Kiddo. Nobody called you a parasite.