Depends if you care in any way about the outcome.

If you in general want to stay, just with a higher compensation, it's good idea to help them rationalize your salary. Especially if your manager will have to argue for you with his boss.

If you simply want a raise and don't care where, indeed that will not benefit you.

I think you and NeverFade actually have different definitions of "justify"

If you can point to where you went above and beyond, which improved the company's bottom line by $X, that will never hurt you in salary negotiations. In that sense, being able to justify your raise strengthens your position.

But you don't have to defend yourself against accusations of sinful greed, or justify why you should earn 3x what teachers or nurses earn. You're talking to someone who is paid more than you, not speaking at a college anarchists' debate about fat cat bosses. You don't need any special justification in that sense.

In such case - you're right. Good CTO should know if what employee requests is within market range for his position. If so - not much point in arguing with the market - it will come to bite you sooner or later.

Personally playing the "I have kids to feed" justification just acts to remind me (coldly) that you can not afford to not be collecting a pay packet from me or someone else.

The market for me is $X, you are paying $X*0.5 - that is unsustainable

It may sound cold, but it's so true. With or without kids, never let others think you have no option

Agreed. I prefer:

"The salary and benefits package I'm given is a direct measure of how much I'm valued as an employee. This other company values me 25% higher".