My commuter would make a squeaking noise while pressing pedals when the chain was on the either of the two smallest cogs, regardless of the chainring.

At first I thought it was the cassette, also my freehub body was wobbling. I relubed everything I could think of, no change. Eventually I got a second set of wheels for winter riding with studded tires and... same thing: different wheel, different hub and cassette; still squeaking. The chain and cassettes were all new, installed at the same time, no stuck/stiff links. The crankset was used but not worn out.

So I replaced the chain and the squeaking is gone. Why would it happen? Both were Shimano 9-sp chains. The cassettes were Shimano Deore 9sp. I mean the problem is gone but I'm wondering what was wrong.

My guess, you got a bad chain, or the factory did not properly lube the inside of the chain. Keep in mind that not all parts off of the same assembly line are equal. Sometimes materials will have weak spots in them. Maybe the lubing machine ran out of lube in the middle of assembling a chain and missed several links, if not the whole chain.

This same thing happens with every thing that is mass produced, there is no way to ensure 100% quality control, most companies aim for less than 2-3% failure/rejects and that is acceptable. Every once in a while something that is not up to snuff makes it into the market.

Yeah, I guess that's one possibility, or it'll remain a mystery I'm soaking that chain in mineral spirits now, then I'll dry it and submerge it in oil for for some time and try again, out of curiosity.