Why is $3$ the coefficient of $n$ in the Collatz conjecture?

Why is $3$ the coefficient of $n$ in the Collatz conjecture?

What's the importance of multiplying a odd number by $3$ and adding $1$,
instead of just adding $1$? After all, if you add $1$ to an odd number
then it turns into an even number.
Here is a example comparing the coefficients $3$ and $1$ (any number could
be used for this, but for simplicity I use $1$)
Using $3n+1$ for the number $27$, there are about $115$ steps.
Using $n+1$ for the number $27$, there are 7 steps.
I know that you could always replace $3$ by any variable you want, but why
did Lothar Collatz make it specifically $3$? Was there some special reason
(maybe his lucky number)? Or would using any other natural number cause
instabilities (which I don't reckon)?