Why is not an iterator an flat_map

I think these two methods are equivalent, but there is an error. What is the reason? Is there a better way to express it?

pub fn create_pair() -> () {
    let vec_num = vec![1, 2, 3];
    let vec_num2 = &vec_num;
    let all = &vec_num
        .iter()
        .flat_map(move |a| vec_num2.iter().map(move |b| [a, b]))
        .collect::<Vec<_>>();

    println!("{:?}", all);
}

[[1, 1], [1, 2], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 2], [3, 3]]

pub fn create_pair() -> () {
    let vec_num = vec![1, 2, 3];
    let all = &vec_num
        .iter()
        .flat_map(move |a| &vec_num.iter().map(move |b| [a, b]))
        .collect::<Vec<_>>();

    println!("{:?}", all);
}

error[E0277]: `&std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>` is not an iterator
 --> src/main.rs:5:10
  |
5 |         .flat_map(move |a| &vec_num.iter().map(move |b| [a, b]))
  |          ^^^^^^^^ `&std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>` is not an iterator
  |
  = help: the trait `std::iter::Iterator` is not implemented for `&std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>`
  = note: required because of the requirements on the impl of `std::iter::IntoIterator` for `&std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>`

error[E0599]: no method named `collect` found for struct `std::iter::FlatMap<std::slice::Iter<'_, {integer}>, &std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>, [closure@src/main.rs:5:19: 5:64 vec_num:_]>` in the current scope
  --> src/main.rs:6:10
   |
6  |           .collect::<Vec<_>>();
   |            ^^^^^^^ method not found in `std::iter::FlatMap<std::slice::Iter<'_, {integer}>, &std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>, [closure@src/main.rs:5:19: 5:64 vec_num:_]>`
   |
   = note: the method `collect` exists but the following trait bounds were not satisfied:
           `&std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>: std::iter::IntoIterator`
           which is required by `std::iter::FlatMap<std::slice::Iter<'_, {integer}>, &std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>, [closure@src/main.rs:5:19: 5:64 vec_num:_]>: std::iter::Iterator`
           `std::iter::FlatMap<std::slice::Iter<'_, {integer}>, &std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>, [closure@src/main.rs:5:19: 5:64 vec_num:_]>: std::iter::Iterator`
           which is required by `&mut std::iter::FlatMap<std::slice::Iter<'_, {integer}>, &std::iter::Map<std::slice::Iter<'_, {integer}>, [closure@src/main.rs:5:48: 5:63 a:_]>, [closure@src/main.rs:5:19: 5:64 vec_num:_]>: std::iter::Iterator`

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