I guess, if you accept the comment, I can make an answer out of it:
~ is an operator in R like +,-, /,*. Although it is possible to use many kinds of characters for your variables using ticks `xxx` and qoute "xxx" you also need to access them with ticks (see ?Reserved). (I'm gonna use quotes instead of ticks here, but consider using ticks for a more accepted style guide.)
R is a functional programming language and therefore you can access every single language statement as a function, e.g. a + b is the same as "+"(a, b). When you write a + b it is just syntactic sugar - language-wise it is translated into a primitive function call with two arguments.
To complicate things, there is an order of evaluation. So if you write a~~b it gets translated into "~"(a, ~b). It is because ~ is a primitive operator desiged as a sigle character. You still can define the function "~~" <- function(a,b) {a + b}, but you can only call it by "~~"(a,b) directly for it to work.
On the other hand, you need to be able to specify how a binary operator looks like. Having defined a function "asdf" <- function(a,b) {a + b} is not enough and this will not work: a asdf b
R has something to define binary operators (R: What are operators like %in% called and how can I learn about them?), see large portion of binary operators used like in magrittr's %>% or doParallel's %dopar%. Thus it is better to stick to the binary operator syntax using %, i.e. <tick>%~~%<tick> <- function(a,b) {a+b}. Then you can easily access it by using syntactic sugar a %~~% b.
Strange stuff, I agree. As for magic tricks: try this at home "for"(a, 1:10, {print(a)}). Bonus question: why is a visible in the parent frame ?