Learn English – “Offensive” vs. “Insulting”

I don't think 'layman' is an offensive term by any account. If you go by OALD, it says...

a person who does not have expert knowledge of a particular subject

So, the term 'layperson' separates a common person from an expert. And, being a 'common man' here does not offend you or me at all.

The example down there puts light on it

a book written for professionals and laymen alike

But I do think that replacing it with 'ordinary' may get a few (including me) some note of offensiveness. I'd use common over ordinary.

However it may be worth noting that (at least in British English) 'layperson' seems to be the more accepted term, likely due to maintaining gender neutrality.

Each indicates a definite property. There is no way around it: the choice will always depend on the power of available parsers.

Either indicates a tentative property. Perhaps the choice depends on the power of available parsers for some formalisms, but other formalisms can be chosen regardless of the power of available parsers.

Admittedly, for the example you gave, the difference is not that great, and each and either can be used almost interchangeably.

Perhaps some better examples:

Each party may lose support given the recent crisis

In this case, any party in our fictional country may see angry voters.

Either party may lose support given the recent crisis

Some parties may lose support, because they handled the situation badly. Other parties may not see an effect, perhaps because their voters don't care about the crisis at hand.