Why does Tom tell Ben Rogers that he likes whitewashing the fence

The Evidence is shown and explained in part B of the question.

Reluctance means 'unwillingness or disinclination to do something', which means that Tom is making it look like he doesn't want to give the brush to him, but with alacrity in his heart which means cheerfulness.

answer:   a good wench, give it me.

iago

good girl, give it to me.

emilia

what will you do with ’t, that you have been so earnest

325to have me filch it?

emilia

and what are you going to do with it? why did you want it so much that you begged me to steal it?

iago

  why, what is that to you?

iago

what’s it to you?

emilia

if it be not for some purpose of import,

give ’t me again. poor lady, she’ll run mad

when she shall lack it.

emilia

if you don’t need it for some important reason, then give it back to me. poor lady, she’ll go crazy when she sees it’s missing.

iago

be not acknown on ’t,

330i have use for it. go, leave me.

iago

don’t admit to knowing anything about it. i need it. now go, leave me.

exit emilia

emilia exits.

i will in cassio’s lodging lose this napkin

and let him find it. trifles light as air

are to the jealous confirmations strong

as proofs of holy writ. this may do something.

335the moor already changes with my poison.

dangerous conceits are in their natures poisons

which at the first are scarce found to distaste,

but with a little act upon the blood

burn like the mines of sulfur.

i’ll leave this handkerchief at cassio’s house and let him find it.to a jealous man, a meaningless little thing like this looks like absolute proof. this handkerchief may be useful to me. the moor’s mind has already become infected with my poisonous suggestions. ideas can be like poisons. at first they hardly even taste bad, but once they get into your blood they start burning like hot lava.

enter othello

othello enters.

    i did say so.

340look, where he comes. not poppy nor mandragora

nor all the drowsy syrups of the world,

shall ever medicine thee to that sweet sleep

which thou owedst yesterday.

here he comes. no drugs or sleeping pills will ever give you the restful sleep that you had last night.

othello

    ha! ha! false to me?

othello

argh! she’s cheating on me?

iago

why, how now, general? no more of that.

iago

oh, general, , no more of that!

explanation:

there is no excerpt.

put the excerpt in the comments and ill answer.