First of all, not everyone emigrates because of hate for their homeland, many do it for necessity and keep close ties.
Some emigrate to search fortune to one day return.
Some emigrate for love, of people or things.
And even those that in the end emigrate because they didn't like their country might still want to fight, not for the country, but for the people that they love that still live in it.
Soon after WWI he and his friends were riding a motorless German motorcycle down a hill and he broke his leg. He never told his dad because he was afraid he'd be beaten.
My grandfather got involved in the Polish mafia and was involved in a ring that was stealing grain from farmers, in the interwar period he had a choice of going to jail or going to the US (where he had citizenship because he was born here) so he came back to Manchester.
Gus was always proud of being Polish in fact he kept going to a Polish church, stayed involved with Polish organized crime, etc. When my dad wanted permission to marry my mom (a challenge because my dad was French Canadian) he was told that Gus was working at the bar on Sunday at the Polaski club (when bars aren't supposed to be open.) My dad figured he was cleaning the tables but when my dad arrived he found the bar was open, Gus was tending it, and two city aldermen were drinking there.
When WWII came along Gus volunteered to fight (to defend Poland and Europe as a whole) but they rejected him because of his broken leg.
So you can be an immigrant to the US, love the US, love the country you came from, love the immigrant community that you're a part of. It all goes together.
People emigrate for a variety of reasons but I suspect two factors cover the majority of reasons: (1) for better opportunities, and (2) for new experiences. Neither of these reasons mean that you don't like the country you originally resided in. Emigrating usually just means that you believe you can build a better life elsewhere.
And maybe before judging people telling them that they don't love their country, you should first put youself in their shoes.