Pro-American Immigration & Anti-American Emigration

This issue has been bothering me for some time because I find it hypocrital, so I have to ask...Why are so many people that support immigration to America against Americans emigrating elsewhere? Having dual citizenship or a second passport is a privilege and can be beneficial in many ways. Why shouldn't Americans also benefit? It's strange when those with backup plans in other countries are adamantly against others also having backup plans.

If your issue with American emigration is possible gentrification and colonization, how do you feel about Americans that feel the same towards American immigration? Many Americans live in communities that have been gentried by newcomers. Are their complaints about this valid?