Weird behaviour with class fields when adding to a std::vector

Your code has undefined behavior. In

void set(){
    X = 3;
    cout << "Before, X = " << X << endl;
    nodes.push_back(Node());
    cout << "After, X = " << X << endl;
}

The access to X is really this->X and this is a pointer to the member of the vector. When you do nodes.push_back(Node()); you add a new element to the vector and that process reallocates, which invalidates all iterators, pointers and references to elements in the vector. That means

cout << "After, X = " << X << endl;

is using a this that is no longer valid.