A one-sided argument is a common bit of rhetorical trickery in which the person making an argument presents evidence for only one side. This is exactly what we expect from advertisers and politicians -- and, increasingly, the media -- so it is generally viewed as socially acceptable in most situations. It is neither a formal nor an informal fallacy, but is it a misleading form of argument, and should be avoided in cases where the truth is more important than the sale.
While we do not usually expect our conversation partners to be balanced and impartial in their opinions, we do generally hope for this from educators, scientists, and, if we are truly idealistic, journalists. Unfortunately, we all prefer a style of communication that suppresses our ability to judge whether we are hearing a balanced view; specifically, we do not want to hear a bunch of evidence and then be left to make our own judgements. We want to hear a conclusion and some of the evidence that supports this conclusion. If we are particularly motivated, some of us might spend some time hearing two competing and contrary conclusions. If we are really motivated, we might even listen to a third.
Broadcast media is not incentivized to pander to the most motivated and interested audience member. So it does not.
It borders on ridiculous to give an example of a one-sided argument. Either you can name 20 examples off the top of your head -- examples you've just heard from the news, advertising, and your uncle Bob -- or you simply don't care. However, I will point you towards a classic example of flip-flopping from one one-sided argument to another: the infamous whiskey speech.
One-sided arguments may also be referred to as cherry-picking (particularly in science and medicine), card stacking, stacking the deck, ignoring the counterevidence, slanting, and suppressed evidence.