"lifetime may not live long enough" vs "second mutable borrow occurs here first borrow later used here"

Question

Rust Lifetime is really a puzzle to me, and here is the problem

#[derive(Debug)]
pub struct Container<'a> {
    contains: Vec<&'a str>,
}

#[derive(Debug)]
pub struct Space<'a> {
    elems: Vec<String>,
    packages: Vec<Container<'a>>,
}

impl<'a> Space<'a> {
    pub fn new() -> Space<'a> {
        Space {
            elems: Vec::new(),
            packages: Vec::new(),
        }
    }

    pub fn increase(&mut self){
        self.elems.push("a".to_string());
        self.elems.push("b".to_string());
        self.elems.push("c".to_string());
        let strings = &self.elems[..3];
        let new_pack= Container{contains: vec![&strings[0],&strings[1],&strings[2]]};
        self.packages.push(new_pack); // error: lifetime may not live long enough
    }
}

The error message is :

error: lifetime may not live long enough
  --> src/lib.rs:82:9
   |
68 | impl<'a> Space<'a> {
   |      -- lifetime `'a` defined here
...
76 |     pub fn increase(&mut self){
   |                     - let's call the lifetime of this reference `'1`
...
82 |         self.packages.push(new_pack);
   |         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ argument requires that `'1` must outlive `'a`

To fix this problem, rewrite as

pub fn increase(&'a mut self){
    self.elems.push("a".to_string());
    self.elems.push("b".to_string());
    self.elems.push("c".to_string());
    let strings = &self.elems[..3];
    let new_pack= Container{contains: vec![&strings[0],&strings[1],&strings[2]]};
    self.packages.push(new_pack);
}

then , this newly introduced lifetime 'a makes the instance of 'Space' cannot be changed anymore.

mod tests{
    use crate::Space;

    // #[test]
    fn test_space(){
        let mut new_space = Space::new();
        new_space.increase();
        new_space.increase(); // error message : cannot borrow `new_space` as mutable more than once at a time
    }
}

error message:

error[E0499]: cannot borrow `new_space` as mutable more than once at a time
  --> src/lib.rs:93:9
   |
92 |         new_space.increase();
   |         -------------------- first mutable borrow occurs here
93 |         new_space.increase();
   |         ^^^^^^^^^^^^^^^^^^^^
   |         |
   |         second mutable borrow occurs here
   |         first borrow later used here

So the common mistake is trying to maintain a set of data and reference of this data in the same structure and hope there is a method that could introduce new data to that structure.