Bdtyk

Consider the word quixotic.

It suggests wishful thinking to the point of lunacy in pursuit of one's ideals.

The novel Don Quixote is about an old man who decides to become a knight even though the days of chivalry had ended long ago. Despite the impracticality of the notion and a great deal of failure and pain, he still continues to attempt to pursue knighthood (and continues to fail over and over again).

The only catch is that this word is typically only applied to a person pursuing a noble but impractical or impossible cause, so you would not typically use this word to describe a persistent bank robber. Be sure to take the context into account when deciding if this word is right for your situation.

The idiomatic phrase grasping at straws may convey the concept

1. trying to find some way to succeed when nothing you choose is likely to work

Jerry, grasping at straws, searched the backup tapes from last week, looking for the missing files.

2. trying to find reasons to feel hopeful about a bad situation

She thinks he might still be interested because he calls her now and then but I think she's clutching at straws.

Cambridge Dictionary of American Idioms cited at thefreedictionary.com

The term flail is also sometimes used

To make energetic but aimless or or ineffectual efforts:

As the end of law school approached, Hill flailed briefly in numerous professional directions

American Heritage

Supplement: Along the lines of the good answer by @pyobum, the phrase cockeyed optimist is sometimes encountered. Merriam-Websters Learners' Dictionary offers this definition of cockeyed

crazy or foolish

Where did you get those cockeyed ideas?

She is full of cockeyed optimism.

The term is the title of a featured song in the musical South Pacific

Delusional (both definitions from Merriam-Webster):

"A persistent false psychotic belief regarding the self or persons or objects outside the self that is maintained despite indisputable evidence to the contrary; also : the abnormal state marked by such beliefs"

[in] Denial:

2: "refusal to admit the truth or reality (as of a statement or charge) (2) : assertion that an allegation is false"

6: "a psychological defense mechanism in which confrontation with a personal problem or with reality is avoided by denying the existence of the problem or reality"

"in denial" : "refusing to admit the truth or reality of something unpleasant"

Possibly relevant:

MW: Monomaniacal

"excessive concentration on a single object or idea"

Like a dog with a bone:

Wiktionary:

Stubborn; persistent; relentless; dogged

The Free Dictionary:

to refuse to stop thinking about or talking about a subject
On the subject of fathers’ rights, he’s like a dog with a bone. 

"Mad hope" is an expression for irrational hope in the face of massive evidence to the contrary. See this Google books search.

You could describe Person A as having an idée fixe. From Wikipedia:

An idée fixe is a preoccupation of mind believed to be firmly resistant to any attempt to modify it, a fixation.

As a less-common French phrase, it may be viewed as slightly pretentious in some circles.

Consider Pollyanna or Pollyannaish, defined as follows by "Dictionary.com Unabridged:"

(often lowercase). unreasonably or illogically
optimistic: some pollyanna notions about world peace.

I'll throw these on the pile:

• They're dreaming


• They're delusional


• They're hoping in vain


• They're living in fairyland


• They believe in fairytales

A bit out of place, but naïve may be what you're looking for, especially for generally describing them.

I think I would use the word lazy (with possibly a seasoning of ignorant - but that is just another kind of laziness).

If they had something more useful to do, they could be doing that, instead. If they understood why they can't do whatever, they would be interested in something else. But understanding how things work and why things are like they are takes effort (as does overcoming obstacles that can be overcome).

But you have to perceive or perhaps encounter the obstacles before you can avoid them.

So... that persistence could instead be a good thing, if they just put some real effort and thought into it. (And I recognize that some people might object that persistence means that the person cannot be lazy - but, in fact, all people are persistent in some sense. This is a part of human nature, and a part of being alive.)

That said, quite likely they are being this way because of something else that they were told. So... who told them that?

I'm by no means an english speaking native, but a more objective wording of what this thing you describe could be : a discrepancy of perception.

What it means is that there is a difference how different people interpret a piece of communication or a situation. What you want to convey is probably that one person does not interpret a message or a situation the same way you do or at least not the same way you expect / want them to.