For example: A situation needs both Fact A and Fact B to be explained, but a person accepts Fact A and rejects Fact B, misconstruing the situation?
Do you think this is just ignorance or deliberate _____?
You can call it a bias. Depending on the person's reason for rejecting fact B, you can use the name of the specific type of bias. For example, if the person chooses fact A over fact B because he already believes in fact A, it's called a confirmation bias.
The tendency to prefer certain facts can be called partiality.
Edit: the relation between the person and the fact they are rejecting can be called denial, and if the person does this often, you can say they engage in denialism.
If the person is aware of the facts and chooses to intentionally disregard them, this is described (originally in legal terms, but also in common usage) as willful ignorance:
Willful ignorance is the state and practice of ignoring any sensory input that appears to contradict one’s inner model of reality. At heart, it is almost certainly driven by confirmation bias.
I like this phrase because it includes the word willful (intentional), which underlines the fact that it's a deliberate choice. To further bring home the point, RationalWiki also notes that:
It is sometimes referred to as tactical stupidity.
To directly answer your question, one might phrase it such:
Do you think he is just unaware, or being willfully ignorant?
I think this is exactly: cherry picking
"Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position." https://en.wikipedia.org/wiki/Cherry_picking
In the recent debate, the candidate disingenuously overlooked the report from the commission refuting their claims.
It refers to a pretense of ignorance or error to overlook or misconstrue an inconvenient fact. It's often (constantly) used by politicians to misinterpret questions asked of them into more favorable forms:
Q: "What about the budget deficit you created?"
A: "The budget deficit? I'm glad you asked; the opposition really has no economic policy and would lead to recession which is why it's essential that we're re-elected."
This is an disingenuous interpretation of the question to allow the speaker to say whatever they like, pretending not to be aware of the intended meaning of the question.
In other contexts, you might use words like Poo poo or handwave or just wave away such facts if the speaker is merely dismissing them out-of-hand, often with a literal hand-wave as if to brush or ward off the speaker's foolish words.
"Is he ignorant or deliberately obtuse?
Obtuse is slow to understand and deliberate sloth in understanding is a fine rhetorical tactic.
Economical with the truth
An excerpt from The Phrase Finder explains it
Conveying an untrue version of events by leaving out the important facts. A euphemism for lying, in short.
Recorded from the 18th century, although rarely used. It was brought into the contemporary language by the UK Cabinet Secretary, Sir Robert Armstrong, who used the phrase during the Australian 'Spycatcher' trial in 1986.
Lawyer: What is the difference between a misleading impression and a lie?
Armstrong: A lie is a straight untruth.
Lawyer: What is a misleading impression - a sort of bent untruth?
Armstrong: As one person said, it is perhaps being "economical with the truth".
How about obfuscation?
obfuscation: to make (something) more difficult to understand
Do you think this is just ignorance or deliberate obfuscation?
deliberate interference with the progress or business especially of a legislative body
"Obstructionism." Merriam-Webster.com. Merriam-Webster, n.d. Web. 26 Oct. 2016.