Like AliceD's answer says, this is a form of forced-choice task used to assay preferences.
These measures are used especially when there is no good counterpart on the opposite side: there is no spectrum to consider. Let's think about your examples:
In general, I prefer [Assertiveness / Clear communication]
I prefer my direct reports to be [Self-directed / Punctual]
What would the "opposite" versions of these be? Some possibilities:
In general, I prefer [Assertiveness / Passiveness]
In general, I prefer [Opaque communication / clear communication]
I prefer my direct reports to be [Self-directed / Micromanaged]
I prefer my direct reports to be [Late / Punctual]
With the exception of maybe the third one (level of oversight), the counterparts are not really that informative. No one wants their employees to be late, but someone might not mind so much if someone is late as long as they manage themselves. The test is trying to get at what your desires are when you weight dissimilar things against each other.
Another example might be food preferences: are sweet and sour opposites?
What about someone that likes, say, fruit flavors - those are both sweet and sour - you need a way to find that someone prefers sweet+sour over savory, or to find that another person likes sweet and savory foods, but doesn't like sour ones.
Other options in this circumstance might be to rank-order possibilities, but in general giving people just 2 options allows them to more quickly make a determination. You can develop rank orders later by analyzing the results of the individual paired items.