You own a car that you paid $10,000 for.
I say, "Cool car! I'll give you $15,000 for it."
You decide not to sell the car.
Did you just make $5000?
Should you have to pay tax on that $5000?
The answers are "No and Hell no!"
You're probably thinking, "Duh. That's obvious!"
If you sold the car, you would have realized the $5000 gain and you would owe taxes on that $5000.
Ditto for stocks.
Also, you owe when you receive a dividend on the stock, as that's "real" money.