The difference between valid arguments, sound arguments, and unsound arguments
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It's important, I think, to distinguish between the notion of validity, which concerns the form of an argument, and soundness, which concerns the truth of an argument. A sound argument is valid, but not all valid arguments are sound. Briefly, validity concerns whether the argument is logically correct, whereas soundness concerns whether the argument is true. A more detailed explanation follows.

Validity refers to the abstract form of an argument. An example is a syllogism:
Major Premise: All X are Y
Minor Premise: a is X
Conclusion: a is Y
A syllogism is valid if the conclusion follows from the premises. If the conclusion does not follow, it is invalid:
Major Premise: All X are Y
Minor Premise: a is Y
Conclusion: a is X
The argument is invalid because the major premise allows for the possibility that there are some elements of Y that are not in X. More formally, X is a could be a proper subset of Y.

Soundness refers to a concrete argument, which must meet two criteria: the argument is valid, and the premises are true.
Major premise: All men are mortal
Minor premise: Mike is a man
Conclusion: Mike is mortal
This argument is sound because it is valid (has the correct form of a valid syllogism), and the premises are true.

An argument is unsound when it is invalid, or a premise is false, or both.
Here's an example of a logically valid but unsound argument because of a false premise:
Major premise: It always rains on my birthday
Minor premise: Today is my birthday
Conclusion: It is raining today
The major premise is false because it is counter-factual: there have been years when it hasn't rained on my birthday. It is also false because there isn't any logical connection between a date being my birthday and rain falling.

Keeping the distinction between validity and soundness in mind can help us when deciding whether an argument is true or false, and to identify why unsound arguments are false, thus making it easier to refute them.
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