Using 'would' to form reasons

Solution 1:

In these,'would' is signalling that the statements are hypothetical or counterfactual.

"Why would anyone want to eat something so horrible?" indicates that you don't expect anyone is going to eat the horrible something.

"Who would live for forever?'indicates that nobody is going live forever.

"Why would I ever lie to you?" indicates that you do not lie to the listener,

Solution 2:

The modal auxiliary verb would was originally the past tense form of the modal will. As such, it has some of the same senses as will, specifically, in this case, that sense of "be willing to" that shows up when will is used in hypothetical clauses:

• if he will put down the gun,

which means if he is willing to put down the gun.

So the rather idiomatic question construction

Wh- would X Infinitive?

means

• Why/Who/When/Where/.. would X be willing to Infinitive?

with the clear implication that the speaker is surprised at the possibility.

Conveying that emotion of surprise is the construction's most important function.
Hence it usually appears as a rhetorical question.