How to convince my father-in-law that stock and crypto gains are legit?

Explain to your FIL how stock gains come from dividends and inflation, not from stealing somebody else's money.

Then point out how much inflation is eating away at his presumably cash savings, and how drastically that puts his retirement in jeopardy.

Crypto is not legit, so don't mention that one.

By that standard, real estate is a sin as well. Like a stock, its price depends entirely on the willingness of the buyer to pay, while its actual value depends on its (or the company's) condition and can go poof at any time. You could receive an insane amount of money for selling it, and the buyer is left with nothing if the house catches on fire the following week.

Owning a stock is owning a business. Would he say owning a business isn't legit? 

It's also a simplistic understanding of the stock market.  He's not taking into consideration things like growth and dividends. 

Stocks grow and markets grow and economies grow. The market as a whole is worth vastly more than it was 100 years ago even if you account for inflation. If you buy a stock at $1 and sell it for $2 and the stock never goes below $2 again, then who lost money? 

Also, dividends. Say there's a stock that sells for $1. You buy it and hold it long enough to earn $1 in dividends. You then sell it for 50 cents. Did you lose money? Even though the stock price dropped by half you still gained 50 cents. 

Forget it. Don't try to convince someone you are "morally" or "ethically" more correct than they are. It never works. Just smile and change the subject. And stop talking about money--it's a recipe for bad feelings. 

I would not try to convince them. Changing someone's beliefs that are engrained on a lifetime of perceptions is not only impossible but could be damaging to the relationship. I would chalk that up there with the list of things not to discuss when opinions differ like politics and religion. You are not going to change someone's political opinion and you cannot make them believe or disbelieve in God. If you have ever tried you know the outcome is never prosperous. Do your thing let them do theirs.

I know how that goes. Convincing someone that stocks are a legit way to make money. I dont do crypto and most on here dont either, so you wont get any support there.  I have 2 ideas that might work, but I wouldnt put much faith in it. Once most people, especially elders, are convinced of something, theres no changing their minds. Those ideas are to show him your account if the gains are impressive and to wave a good amount of real cash that you made off of stocks in front of his face.  You are most likely playing a losing game, so Id just give up on it. I hope you have better things to do.

Explaining the stock market to someone who does not grasp economic basics will be an uphill battle. So many Yahoo! users also seem to think that if one man makes a profit or if a stock's value declines another has had their money stolen, I've tried to explain the fallacy many times with no success. Many seem to think that if you buy a stock for $100 dollars and sell it for $10 that someone took $90 from them, which is absurd. The value of something is only what someone will pay for it on that day.

On the cypto though, that is not an investment. It is a wager on a bet. Unlike shares in a company, there is nothing tangible to back up crypto. No intrinsic value.

Stocks aren't a zero sum game.  If I make $100, that doesn't mean someone else lost $100.  It means the value (or at least perceived value) went up.  If this is what your father-in-law actually believes, then don't take any financial advise from him.  

PS:  Cypto has no real value backing it.  It just gambling.

I would not bring the subject up.  That being said, both you and your FIL are under a few misconceptions.  He is wrong in his belief that for each sale at a gain, someone else loses money.  That not how stock sales work.  Meanwhile, you are wrong about investing being a way of saving money.  You can easily lose some or all of your principal while investing.  That is almost impossible in FDIC insured savings.  Losing principal is especially possible with highly speculative investments such as crypto.  

"Any ideas how to convince my in-laws that investing is actually moral and legit"

Why?   They are entitled to their own opinions even if you disagree.   What they do with their money is none of your business and what you do with your money is none of their business.    These are your in-laws; learn when to keep your mouth shut.