Why do polyneuropathies affect the extremities first?
Polyneuropathy is actually not a very specific term, so the reasons will no doubt vary depending on which specific class you are talking about.

That said, here are two reasons that longer neurons are preferentially affected: 


Some polyneuropathies involve conduction problems that include "failures" where action potentials aren't propagated down the full length. It doesn't matter where along an axon the failure occurs, and longer axons therefore have more "chances" to fail.
Axons are somewhat isolated from the soma where most proteins are created, and it is common in certain neuropathies for degradation to begin furthest from the soma, presumably because the neuron has less capability to deal with problems or repair damage in those areas far from the soma. Neurons with longer axons by definition will have some part of their axons that are further from the soma than neurons with shorter axons. This is the answer that is most relevant to your question, see for example this source that reviews the causes of diabetic neuropathy.




References:

Yagihashi, S., Mizukami, H., &amp; Sugimoto, K. (2011). Mechanism of diabetic neuropathy: where are we now and where to go?. Journal of diabetes investigation, 2(1), 18-32.