Word or phrase describing situation where adequately addressing "X is not harmful" involves a self-destructive proof

Solution 1:

That situation is a dilemma.

ODO:

dilemma NOUN

1 A situation in which a difficult choice has to be made between two or more alternatives, especially equally undesirable ones.

‘His dilemma rests in the choice between telling a lie and losing his chance to marry the woman he loves.’
‘He was given two tough choices, a dilemma that he didn't wish to have.’

Also, catch-22 may work.

ODO:

catch-22 NOUN

A dilemma or difficult circumstance from which there is no escape because of mutually conflicting or dependent conditions.

‘There's always been a bit of a catch 22 about golf - you need to have a handicap to join a club, yet it's very difficult to get that handicap in a civilised way without spending hours on a rain sodden driving range in some murky British suburb.’

Solution 2:

I might describe B as being:

• guilted or manipulated into a lose-lose situation.
• argued or painted into a corner.
• coerced into a no-win situation.
• goaded into a poor decision, just to prove a point.
• a pawn in A's game. (Chess analogy implies sacrifice and manipulation.)

However, I find the cartoon scenario slightly different than the other examples. In the cartoon, it doesn't seem that A or B has ill motives. If you focus on the fact that there's a burning question to be answered, it seems appropriate to say that curiosity killed the cat. Or the wildebeest. If you focus on the fact that there is a debate (still no ill motives), maybe for the sake of argument, B fell on his sword to prove his point.

Solution 3:

You can call it guilt tripping :

Guilt trip

VERB: to make (someone) feel guilty, especially in order to induce them to do something. (ODO)

NOUN: a strong feeling of being guilty that makes you behave in a particular way. (MMD)

He guilt tripped me into going to the party and doing heroin.