meaning - How should I use "infer"?

A recent question on Meta discussed advantages and disadvantages of using more advanced words in ELL. As example, this answer was used:

'A Japanese' infers the Japanese person is a thing, and not a person. This is what deems it offensive.

'A Japanese Person' infers the Japanese person is just that - a person, and is therefore considered fine for use.

While the conclusion of the discussion is not related to this question, one comment disturbed me:

Unhappily, both words are misused there! – StoneyB 18 hours ago

Not to bundle two unrelated words and two different errors, let's focus on infers here. What is the misuse in the example? How should that word be used here correctly?

Answer

To infer is to understand or realize a fact that is not immediately obvious. To imply is to "say something without saying it", so to speak; when you imply something, you are indicating it to be true without ever actually saying it outright. You infer what I imply; I infer what you imply.

So, to put it in context, the phrase "A Japanese" may imply something offensive, but you, as a listener or reader, have inferred this.